This paper presents a novel approach for indoor acoustic source localization using microphone arrays, based on a Convolutional Neural Network (CNN). In the proposed solution, the CNN is designed to directly estimate the three-dimensional position of a single acoustic source using the raw audio signal as the input information and avoiding the use of hand-crafted audio features. Given the limited amount of available localization data, we propose, in this paper, a training strategy based on two steps. We first train our network using semi-synthetic data generated from close talk speech recordings. We simulate the time delays and distortion suffered in the signal that propagate from the source to the array of microphones. We then fine tune this network using a small amount of real data. Our experimental results, evaluated on a publicly available dataset recorded in a real room, show that this approach is able to produce networks that significantly improve existing localization methods based on SRP-PHAT strategies and also those presented in very recent proposals based on Convolutional Recurrent Neural Networks (CRNN). In addition, our experiments show that the performance of our CNN method does not show a relevant dependency on the speaker’s gender, nor on the size of the signal window being used.