In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing with the signal reconstruction problem was proposed by Griffin and Lim. This method usually requires many iterations for the signal reconstruction process and depending on the inputs, it does not always produce high-quality audio signals. To overcome these shortcomings, we apply a learning-based approach to the signal reconstruction problem by modeling the signal reconstruction process using a deep neural network and training it using the idea of a generative adversarial network. Experimental evaluations revealed that our method was able to reconstruct signals faster with higher quality than the Griffin-Lim method.