This paper presents an efficient numerical method for solving the Cahn–Hilliard equation with a data assimilation term. The data assimilation term uses a feedback control strategy to guide the computational solution toward observed data. The Crank–Nicolson formula is used for discretizing the equation system, while a scalar auxiliary variable approach ensures energy dissipation preservation. The proposed scheme achieves second-order accuracy in both time and space. Theoretical proof confirms the unconditional energy stability of the scheme. Numerical experiments demonstrate the effectiveness of the proposed method. The Cahn–Hilliard equation is widely used in various fields, including tumor growth, spinodal decomposition, and multiphase fluid flow. Previous studies have focused on improving simulations of the equation. However, in some scenarios, the governing equation may involve unknown mechanisms, and missing initial conditions complicate the problem. Therefore, directly applying existing methods may lead to significant deviations from the actual process. Advances in sensor technology allow the acquisition of observed data from real processes. Data assimilation methods, inspired by weather prediction, have been extensively studied for various partial differential equations. These methods can be classified into three categories: Bayesian methods, variational frameworks, and nudging approaches. While these methods have been widely applied, they still face issues such as stability, accuracy, and computational cost. The nudging method, which is the focus of this paper, is a flexible and tractable data assimilation technique. It adds an extra feedback control term to the governing equation, driving the system state variables toward observed values. The nudging method has been used for initializing hurricane models and solving dissipative nonlinear PDEs. It has been shown to ensure convergence of approximating solutions to reference solutions over time. The method is also effective for various other equations, including the Navier–Stokes equation and surface quasi-geostrophic equation. The paper demonstrates the effectiveness of the proposed method through numerical experiments.This paper presents an efficient numerical method for solving the Cahn–Hilliard equation with a data assimilation term. The data assimilation term uses a feedback control strategy to guide the computational solution toward observed data. The Crank–Nicolson formula is used for discretizing the equation system, while a scalar auxiliary variable approach ensures energy dissipation preservation. The proposed scheme achieves second-order accuracy in both time and space. Theoretical proof confirms the unconditional energy stability of the scheme. Numerical experiments demonstrate the effectiveness of the proposed method. The Cahn–Hilliard equation is widely used in various fields, including tumor growth, spinodal decomposition, and multiphase fluid flow. Previous studies have focused on improving simulations of the equation. However, in some scenarios, the governing equation may involve unknown mechanisms, and missing initial conditions complicate the problem. Therefore, directly applying existing methods may lead to significant deviations from the actual process. Advances in sensor technology allow the acquisition of observed data from real processes. Data assimilation methods, inspired by weather prediction, have been extensively studied for various partial differential equations. These methods can be classified into three categories: Bayesian methods, variational frameworks, and nudging approaches. While these methods have been widely applied, they still face issues such as stability, accuracy, and computational cost. The nudging method, which is the focus of this paper, is a flexible and tractable data assimilation technique. It adds an extra feedback control term to the governing equation, driving the system state variables toward observed values. The nudging method has been used for initializing hurricane models and solving dissipative nonlinear PDEs. It has been shown to ensure convergence of approximating solutions to reference solutions over time. The method is also effective for various other equations, including the Navier–Stokes equation and surface quasi-geostrophic equation. The paper demonstrates the effectiveness of the proposed method through numerical experiments.