This article proposes a tensor decomposition-based method for channel estimation in movable-antenna (MA) MIMO systems, aiming to achieve high accuracy with low pilot training overhead. The method involves a two-stage Tx-Rx successive antenna movement pattern for pilot training, allowing the received pilot signals to be expressed as a third-order tensor. The tensor is then decomposed using canonical polyadic (CP) decomposition to obtain factor matrices, which are used to estimate the parameters of multi-path channel components, including their azimuth and elevation angles and complex gain coefficients. This enables the reconstruction of the wireless channel between any pair of Tx and Rx MA positions. The uniqueness condition of the tensor decomposition is analyzed to ensure accurate and efficient channel reconstruction based on measurements at a finite number of Tx/Rx MA positions. Simulation results demonstrate that the proposed method outperforms existing methods in terms of channel estimation accuracy and pilot overhead. The method leverages the intrinsic multidimensional signal characteristics of MA-based channels to achieve efficient channel estimation and reconstruction, significantly reducing the pilot training overhead while maintaining high accuracy. The approach is validated through simulations showing that the proposed method achieves lower normalized mean square error (NMSE) compared to benchmark algorithms, especially when the pilot training area is small. The results highlight the effectiveness of the tensor decomposition-based approach in MA-enabled MIMO systems.This article proposes a tensor decomposition-based method for channel estimation in movable-antenna (MA) MIMO systems, aiming to achieve high accuracy with low pilot training overhead. The method involves a two-stage Tx-Rx successive antenna movement pattern for pilot training, allowing the received pilot signals to be expressed as a third-order tensor. The tensor is then decomposed using canonical polyadic (CP) decomposition to obtain factor matrices, which are used to estimate the parameters of multi-path channel components, including their azimuth and elevation angles and complex gain coefficients. This enables the reconstruction of the wireless channel between any pair of Tx and Rx MA positions. The uniqueness condition of the tensor decomposition is analyzed to ensure accurate and efficient channel reconstruction based on measurements at a finite number of Tx/Rx MA positions. Simulation results demonstrate that the proposed method outperforms existing methods in terms of channel estimation accuracy and pilot overhead. The method leverages the intrinsic multidimensional signal characteristics of MA-based channels to achieve efficient channel estimation and reconstruction, significantly reducing the pilot training overhead while maintaining high accuracy. The approach is validated through simulations showing that the proposed method achieves lower normalized mean square error (NMSE) compared to benchmark algorithms, especially when the pilot training area is small. The results highlight the effectiveness of the tensor decomposition-based approach in MA-enabled MIMO systems.