An effective finite control set model predictive control (FCS‐MPC) is introduced for single‐phase three‐level T‐type rectifiers supplying resistive as well as constant power loads (CPL). The main problem of CPL is the negative resistance phenomenon that endangers the rectifier's stability. Hence, the proposed FCS‐MPC method is based on Lyapunov's stability theory such that the stability of the rectifier is guaranteed under all operating points. Unlike the existing FCS‐MPC methods, the cost function design in the proposed control method is formulated on the rectifier's stability. According to Lyapunov's stability theory, the rectifier stays stable provided that the rate of change of Lyapunov function is negative. In this case, the derivative of the Lyapunov function can be used as the cost function without utilizing any weighting factor. Therefore, contrary to the existing FCS‐MPC methods, the weighting factor requirement is eliminated which leads to easiness in the design and implementation of the controller. Experimental results reveal that the proposed control approach exhibits very good performance with undistorted and distorted grid voltage conditions when the rectifier feeds resistive and CPL loads.