In this paper we propose a stochastic model predictive control method for discrete linear unmanned aerial vehicle (UAV) guidance system with additive total disturbance. The velocity constraint is given in the form of two-sided joint chance constraint, while the acceleration constraint is a hard constraint. Based on the Boole’s inequality and known probability distribution, we propose a deterministic convex transformation method for chance constraint. Subsequently, a stochastic model predictive control algorithm is derived. The effectiveness of the proposed algorithm is verified through a numerical simulation example.