A four-wheel ground vehicle has three body-dominated motion-modes, that is, bounce, roll, and pitch motion-modes. Real-time identification of these motion-modes can make vehicle suspensions, in particular, active suspensions, target on the dominant motion-mode and apply appropriate control strategies to improve its performance with less power consumption. Recently, a motion-mode energy method (MEM) was developed to identify the vehicle body motion-modes. However, this method requires the measurement of full vehicle states and road inputs, which are not always available in practice. This paper proposes an alternative approach to identify vehicle primary motion-modes with acceptable accuracy by employing neural networks (NNs). The effectiveness of the trained NNs is verified on a 10-DOF full-car model under various types of excitation inputs. The results confirm that the proposed method is effective in determining vehicle primary motion-modes with comparable accuracy to the MEM method. Experimental data is further used to validate the proposed method.