Global Navigation Satellite System (GNSS) is pervasively used in position, navigation, and timing (PNT) applications. As a consequence, important assets have become vulnerable to intentional attacks on GNSS, where of particular relevance is spoofing transmissions that aim at superseding legitimate signals with forged ones in order to control a receiver’s PNT computations. Detecting such attacks is therefore crucial, and this article proposes to employ an algorithm based on deep learning to achieve the task. A data-driven classifier is considered that has two components: a deep learning model that leverages parallelization to reduce its computational complexity, and a clustering algorithm that estimates the number and parameters of the spoofing signals. Based on the experimental results, it can be concluded that the proposed scheme exhibits superior performance compared to the existing solutions, especially under moderate-to-high signal-to-noise ratios.