Smooth particle hydrodynamics(SPH) method is a Lagrangian meshless approach that offers unique advantages for simulating solid impact dynamics involving nonlinear large deformation of materials at high strain rates. However, the SPH method suffers from computational instability, stress oscillation, and deformation distortion. To address these issues and enhance computational accuracy, this paper proposes a novel SPH method based on the Harten-Lax-van Leer-Contact(HLLC) Riemann solver. This method employs a three-wave model to solve the Riemann solutions of stresses and velocities in the star region on both sides of the intermediate region, while controlling dissipation through a thermal softening-based limiter. Numerical tests involving structural impacts at different strain rates demonstrate that this method can accurately resolve plastic deformation during impact dynamics and produce smooth and precise stress fields. The SPH method based on the HLLC Riemann solver proposed in this paper improves the computational accuracy of the strong plastic deformation of materials and helps to extend the application of the SPH method in the field of impact dynamics.