This letter introduces a deep learning (DL) framework for direction-of-arrival (DOA) estimation. Previous works in DL context mostly consider a single or two target scenario which is a strong limitation in practice. Hence, in this work, we propose a DL framework for multiple signal classification (DeepMUSIC). We design multiple deep convolutional neural networks (CNNs), each of which is dedicated to a subregion of the angular spectrum. In particular, each CNN is fed with the array covariance matrix and it learns the MUSIC spectra of the corresponding angular subregion. We have shown, through simulations, that the proposed DeepMUSIC framework has superior estimation accuracy and exhibits less computational complexity in comparison with both DL and non-DL based techniques.