The biological network has a complex structure, neurons in the brain are connected recurrently and transmit information through the spikes. Therefore, the recurrent spiking neural network with feedback connection can better simulate the information processing process of the brain. In this paper, combining the feedback alignment and spike timing-dependent plasticity mechanisms, we present a supervised learning algorithm for recurrent spiking neural networks, named FA-STDP. In experiments, we applied the proposed algorithm to spike train learning and nonlinear pattern classification problems to verify its effectiveness, and analyzed the influence of different parameters on the learning process. The results show that the FA-STDP algorithm has good learning performance for spatio-temporal pattern recognition.