This paper considers the fully complex backpropagation algorithm (FCBPA) for training the fully complex-valued neural networks. We prove both the weak convergence and strong convergence of FCBPA under mild conditions. The decreasing monotonicity of the error functions during the training process is also obtained. The derivation and analysis of the algorithm are under the framework of Wirtinger calculus, which greatly reduces the description complexity. The theoretical results are substantiated by a simulation example.