Deep neural network (DNN) have become a popular means of separating a target source from a mixed signal. Most of DNN-based methods modify only the magnitude spectrum of the mixture. The phase spectrum is left unchanged, which is inherent in the short-time Fourier transform (STFT) coefficients of the input signal. However, recent studies have revealed that incorporating phase information can improve the quality of separated sources. To estimate simultaneously the magnitude and the phase of STFT coefficients, this work paper developed a fully complex-valued deep neural network (FCDNN) that learns the nonlinear mapping from complex-valued STFT coefficients of a mixture to sources. In addition, to reinforce the sparsity of the estimated spectra, a sparse penalty term is incorporated into the objective function of the FCDNN. Finally, the proposed method is applied to singing source separation. Experimental results indicate that the proposed method outperforms the state-of-the-art DNN-based methods.