A GPC (generalised predictive control) algorithm which is robust to disturbances is proposed. This control algorithm is derived with constrained terminal output weightings using a standard cost function of linear quadratic discrete game theory. The solution is obtained from the min-max problem which can be solved by discrete game theory and has nonrecursive forms which do not use the Riccati equations. It is derived for both finite and infinite terminal output weightings. To improve the possibility of the existence of a solution for robust constrained GPCs, a modified robust GPC algorithm which uses a different cost function from the standard one is also presented. The usefulness of the proposed controllers is demonstrated by computer simulations.