We present a reformulation of the model predictive control problem using a Legendre basis. To do so, we use a Legendre representation both for prediction and optimization. For prediction, we use a neural network to approximate the dynamics by mapping a compressed Legendre representation of the control trajectory and initial conditions to the corresponding compressed state trajectory. We then reformulate the optimization problem in the Legendre domain and demonstrate methods for including optimization constraints. We present simulation results demonstrating that our implementation provides a speedup of 31-40 times for comparable or lower tracking errors with or without constraints on a benchmark task.