A new evolutionary algorithm is introduced for training both feedforward and recurrent neural networks. The proposed approach, called the Family Competition Evolutionary Algorithm (FCEA), automatically achieves the balance of the solution quality and convergence speed by integrating multiple mutations, family competition and adaptive rules. We experimentally analyse the proposed approach by showing that its components can cooperate with one another, and possess good local and global properties. Following the description of implementation details, our approach is then applied to several benchmark problems, including an artificial ant problem, parity problems and a two-spiral problem. Experimental results indicate that the new approach is able to stably solve these problems, and is very competitive with the comparative evolutionary algorithms.