Salp Swarm Algorithm (SSA) is a novel meta-inspired optimization algorithm. The main inspiration of this algorithm is the swarming behavior of salps when navigating and foraging in the ocean. This algorithm has already displayed the strong ability in solving some engineering design problems. This paper proposes an improved salp swarm algorithm based on simplex method named as simplex method-based salp swarm algorithm (SMSSA). The simplex method is a stochastic variant strategy, which increases the diversity of the population and enhances the local search ability of the algorithm. This approach helps to achieve a better trade-off between the exploration and exploitation ability of the SSA and makes SSA more robust and faster. The proposed algorithm is compared with other four meta-inspired algorithms on 4 benchmark functions. The proposed algorithm is also applied to one real-life constrained engineering design problems. The experimental results have demonstrated the MSSSA performs better than the other competitive meta-inspired algorithms.