Neural decoding involves correlating signals acquired from the brain to variables in the physical world like limb movement or robot control in Brain Machine Interfaces. In this context, this work starts from a specific pre-existing dataset of neural recordings from monkey motor cortex and presents a Deep Learning-based approach to the decoding of neural signals for grasp type classification. Specifically, we propose here an approach that exploits LSTM networks to classify time series containing neural data (i.e., spike trains) into classes representing the object being grasped. The main goal of the presented approach is to improve over state-of-the-art decoding accuracy without relying on any prior neuroscience knowledge, and leveraging only the capability of deep learning models to extract correlations from data. The paper presents the results achieved for the considered dataset and compares them with previous works on the same dataset, showing a significant improvement in classification accuracy, even if considering simulated real-time decoding.