The Mayfly Algorithm (MA), which serves as a new swarm intelligence optimization algorithm, proves to perform well in optimization. However, when it comes to complex problems related to high dimensions and linearity, MA is still prone to premature convergence. Thus, a new mayfly algorithm based on inversion variation (Inversion Variation Mayfly Algorithm, IVMA) is proposed. IVMA, which changes the operation of the original MA on mutation, stochastically selects the random dimension of an individual to approach that of the global optimal individual. In addition, it retains the evolution results with the elite strategy. The inversion operation is used to reverse the position of the optimal individual in a certain dimension segment, which enhances the ability of the algorithm to jump out of the local optimum. The results from ten test functions indicate that IVMA has high convergence accuracy and improved convergence performance.