This paper explores the use of neural networks to control robots in tasks requiring sequential and learning behavior. We propose a family competition evolutionary algorithm (FCEA) to evolve networks that can integrate these different types of behavior in a smooth and continuous manner. The approach integrates self-Adaptive Gaussian mutation, self-Adaptive Cauchy mutation, decreasing-based Gaussian mutation, and family competition. In order to illustrate the power of the approach, we apply this approach to two different task domains: The artificial ant problem and a sequential behavior problem-an agent learns to play football. From the experimental results, we find our approach performs much better than other evolutionary algorithms in these two tasks. Based on the results from our experiments, it is shown that our approach can evolve neural networks to provide a means of integrating, sequencing and learning within a single control system.