We propose a robust tube-based Model Predictive Control (MPC) paradigm for nonlinear systems whose dynamics can be expressed as a difference of convex functions. The approach exploits the convexity properties of the system model to derive convex conditions that govern the evolution of robust tubes bounding predicted trajectories. These tubes allow an upper bound on a performance cost to be minimised subject to state and control constraints as a convex program, the solution of which can be used to update an estimate of the optimal state and control trajectories. This process is the basis of an iteration that solves a sequence of convex programs at each discrete time step. We show that the algorithm is recursively feasible, converges asymptotically to a fixed point of the iteration and ensures closed loop stability. The algorithm can be terminated after any number of iterations without affecting stability or constraint satisfaction. A case study is presented to illustrate an application of the algorithm.