To overcome the shortcomings of the basic shuffled frog leaping algorithm (SFLA), such as slow convergence speed, low optimization precision and falling into local optimum easily, etc., we propose a novel coevolutionary shuffled frog leaping algorithm (CSFLA). As for the local search strategy of the proposed algorithm, we introduce the average value and make full use of the best individuals to update the worst frog individuals in the subgroup, which expands the searching space effectively and increases the diversity of population. Meanwhile, the interactive learning strategy for a small number of worse frog individuals in the subgroup is adopted to learn from the best frog individuals in neighboring subgroups, which increases the frequency of interaction between subgroups and improves the degree of information sharing, thus conducive to algorithm evolution. In the process of global iteration, we adopt the elite group self-learning mechanism to search through the elite space for a better solution, which can further improve the ability of global optimization and lead the evolution of algorithm for the better. Experimental results show that the proposed algorithm can converge to the optimal solution 0 in the seven test functions, and the success rate is 100%, which is better than the other comparative algorithms. The proposed algorithm can effectively avoid premature convergence, and greatly improve the convergence speed and the accuracy of the algorithm.