The algorithm of sine and cosine has some problems such as premature convergence, low accuracy and slow speed for solving high-dimensional functions. This paper proposes an improved sine and cosine algorithm based on hybrid mutation strategy. Firstly, the initial population was generated by the chaotic initialization strategy to improve the diversity of the initial population. Secondly, the hybrid mutation is used to perturb the population, which improves the convergence precision of the algorithm and enhances the ability to jump out of the local optimum. Finally, the boundary control strategy is designed to regenerate the population beyond the boundary. Ten standard test functions are analyzed by numerical simulation and compared with other algorithms to verify the effectiveness of the proposed algorithm. The improved sine and cosine algorithm proposed in this paper is applied to pressure vessel design problems to verify the effectiveness of the improved algorithm in solving practical problems.