In the past, the limited real-time computing power has mostly restricted the neural networks to the shallow type. In this paper, the speed observers for permanent magnet synchronous motors are considered. Deep neural networks, i.e., multiple hidden layers with relatively larger neuron numbers, are designed in conjunction with the classical sliding mode observers. The preliminary investigation shows that transfer learning, i.e., re-training the simulation data-trained deep neural networks using experimental data, can significantly improve the experimental performance. Both the simulation and experimental results indicate that the deep neural networks can offer a data-driven alternative to mitigating speed estimate chattering while maintaining the known sliding mode observer’s advantages of simple parameter design, fast convergence, and good robustness against measurement errors. The work is a proof-of-concept study that confirms the usability of large neural networks in improving the classical sliding mode observers and provides empirical evidence on the training and performance.