This paper presents a family of non-oscillatory, second-order, central difference approximations for nonlinear systems of hyperbolic conservation laws. These approximations are based on the Lax-Friedrichs (LxF) solver and high-resolution MUSCL-type interpolants. The main advantage of this approach is its simplicity, as it avoids solving Riemann problems and field-by-field decompositions. The main disadvantage is the excessive numerical viscosity typical of the LxF solver, which is compensated by using high-resolution MUSCL-type interpolants. Numerical experiments show that the results obtained by this method are comparable to those of upwind schemes. The paper is organized into sections discussing the scalar case, extension to systems of conservation laws, and numerical experiments. In the scalar case, the method is shown to satisfy the Total Variation Diminishing (TVD) property and a cell entropy inequality, ensuring convergence to the unique entropy solution. For systems of conservation laws, the method is extended by using component-wise and characteristic-based approaches. The component-wise approach is used for robust sound waves, while the characteristic-based approach is used for contact waves, where the Artificial Compression Method (ACM) is employed. A corrective type ACM is also introduced to improve contact resolution while maintaining the simplicity of the Riemann-solver-free scalar approach. Numerical experiments with the high-resolution non-oscillatory central difference schemes show that the results are in agreement with the resolution expected by the scalar analysis. The method is found to be easy to implement, robust, and efficient, performing well compared to upwind-based schemes. The paper concludes that the proposed method provides a reliable and efficient way to approximate hyperbolic conservation laws with high resolution and non-oscillatory properties.This paper presents a family of non-oscillatory, second-order, central difference approximations for nonlinear systems of hyperbolic conservation laws. These approximations are based on the Lax-Friedrichs (LxF) solver and high-resolution MUSCL-type interpolants. The main advantage of this approach is its simplicity, as it avoids solving Riemann problems and field-by-field decompositions. The main disadvantage is the excessive numerical viscosity typical of the LxF solver, which is compensated by using high-resolution MUSCL-type interpolants. Numerical experiments show that the results obtained by this method are comparable to those of upwind schemes. The paper is organized into sections discussing the scalar case, extension to systems of conservation laws, and numerical experiments. In the scalar case, the method is shown to satisfy the Total Variation Diminishing (TVD) property and a cell entropy inequality, ensuring convergence to the unique entropy solution. For systems of conservation laws, the method is extended by using component-wise and characteristic-based approaches. The component-wise approach is used for robust sound waves, while the characteristic-based approach is used for contact waves, where the Artificial Compression Method (ACM) is employed. A corrective type ACM is also introduced to improve contact resolution while maintaining the simplicity of the Riemann-solver-free scalar approach. Numerical experiments with the high-resolution non-oscillatory central difference schemes show that the results are in agreement with the resolution expected by the scalar analysis. The method is found to be easy to implement, robust, and efficient, performing well compared to upwind-based schemes. The paper concludes that the proposed method provides a reliable and efficient way to approximate hyperbolic conservation laws with high resolution and non-oscillatory properties.