Various model-based mass estimation approaches have been discussed for a long time. However, estimation performance often deteriorates in some driving situations and, in particular, slow convergence and excessive overshoot of estimates are a major issue for model-based approaches. Meanwhile, mass estimation approaches using ANN models have recently emerged to propose better solutions, but their usefulness has not been fully investigated. Therefore, this paper presents a vehicle mass estimation strategy using practical supervisory artificial neural networks to achieve more accurate results with better convergence. Here, the perturbed engine torque and vehicle longitudinal acceleration are selected as the inputs of the ANN (instead of the original engine torque and vehicle acceleration), which allows for the faster convergence of estimates with high accuracy; these inputs are existing sensor values already available in the vehicle system. The effectiveness of the proposed ANN approach was verified using simulation and software-in-the-loop simulation (SILS) with field test data, and it was found that the convergence speed of the proposed ANN is almost twice as fast as that of the model-based approach, the accuracy is much better, and the estimation quality is constantly stable without any excessive transient responses. This study will provide further insights into mass estimation using the ANN approach.