RBMO (red-billed blue magpie optimizer) has strong global search and fast convergence capabilities, but has low convergence accuracy and insufficient local development performance. To address this issue, IRBMO (improved red-billed blue magpie optimizer) fused with multiple strategies was proposed. Firstly, the good nodes set model was introduced in the initial generation stage of the population to increase the diversity of the red-billed blue magpie population in the early stage. Secondly, the Weibull distribution mutation strategy was utilized to optimize the search step size to improve the individual’s position update strategy, thereby enhancing the convergence speed and accuracy of the algorithm. Finally, a somersault foraging strategy was employed to solve the problem of falling into local traps at the end of the algorithm and not being able to obtain the optimal solution. Numerical experiments were conducted based on twelve benchmark test functions, comparing the algorithm with six other algorithms, the results show that the improved algorithm significantly accelerated convergence speed, improved search accuracy, and achieved better mean and standard deviation,the optimal value error was reduced by an average of 97.96% compared to the original algorithm. Furthermore, the IRBMO was applied to optimize the parameters of the HKELM (hybrid kernel extreme learning machine) model for SOC (state of charge) prediction of lithium-ion batteries. The results demonstrate that the mean absolute error, root mean squared error, and mean absolute percentage error of the model are reduced to 0.58%, 0.75%, and 1.06%, respectively, which further verifies the reliability and effectiveness of the proposed algorithm.