In order to solve the problems of SHO (seahorse optimization), such as low accuracy, precocity and insufficient global search ability. MSHO (multi-strategy seahorse optimization) algorithm based on nonlinear inertial weight strategy, improved whale encircling strategy and improved sine and cosine strategy was MSHO designed. Firstly, the nonlinear inertia weight was introduced into the motion behavior of SHO algorithm to overcome the shortcoming that the algorithm is prone to premature convergence. Secondly, the improved strategy of whale encircling prey was introduced into the updated equation of seahorse hunting success to reduce the probability of the algorithm falling into the local optimal solution. Then, the improved sine-cosine strategy was introduced into the reproduction behavior of the algorithm to enhance the quality of the hippocampal progeny solution, and further improve the global optimization ability and stability of the algorithm. Finally, in order to evaluate the performance of the proposed MSHO algorithm, SHO algorithm, chaotic SHO algorithm, subtraction average algorithm, gray Wolf algorithm, Seagull algorithm, whale optimization algorithm, particle swarm algorithm and MSHO algorithm were compared on 23 benchmark test functions. The experimental results show that MSHO algorithm shows higher convergence accuracy on 20 functions and stronger stability on 16 functions compared with other 7 algorithms. In addition, in order to test the application ability of MSHO algorithm in engineering problems, the algorithm is applied to solve the design problems of welded beams, cantilever beams and pressure vessels. The experimental results show that MSHO algorithm has better search accuracy in these three kinds of engineering design problems than other 7 different algorithms.