We present neural differentiable predictive control (DPC) method for learning constrained neural control policies for uncertain linear systems. DPC is formulated as a differentiable problem whose computational graph architecture is inspired by classical model predictive control (MPC) structure. In particular, the optimization of the neural control policy is based on automatic differentiation of the MPC loss function through a differentiable closed-loop system dynamics model. We show that DPC can learn constrained neural control policies to stabilize systems with unstable dynamics, track time-varying references, and satisfy state and input constraints without the prior need of a supervisory MPC controller.