This paper proposes a robust self-triggered MPC algorithm for a class of constrained linear systems subject to bounded additive disturbances, in which the inter-sampling time is determined by a fast convergence self-triggered mechanism. The main idea of the self-triggered mechanism is to select a sampling interval so that a rapid decrease in the predicted costs associated with optimal predicted control inputs is guaranteed. This allows for a reduction in the required computation without compromising performance. A set of minimally conservative constraints is imposed on nominal states to ensure robust constraint satisfaction. A multi-step open-loop MPC optimization problem is formulated, which ensures recursive feasibility. The closed-loop system is guaranteed to satisfy a mean-square stability condition. To further reduce the computational load, when states reach a predetermined neighbourhood of the origin, the control law of the robust self-triggered MPC switches to a self-triggered local controller. A compact set in the state space is shown to be robustly asymptotically stabilized. Numerical comparisons are provided to demonstrate the efficiency of the strategies