This article introduces a parallel neural network approach implemented over Graphic Processing Units (GPU) to solve a facial recognition problem, which consists in deciding where the face of a person in a certain image is pointing. The proposed method uses the parallel capabilities of GPU in order to train and evaluate a neural network used to solve the abovementioned problem. The experimental evaluation demonstrates that a significant reduction on computing times can be obtained allowing solving large instances in reasonable time. Speedup greater than 8 is achieved when contrasted with a sequential implementation and classification rate superior to 85 % is also obtained.