Different from the vehicles and robots that move on the ground, complex and nonlinear track–wall interactions bring considerable difficulties to the accurate control of tracked wall-climbing robots due to the effect of gravity and adsorption. In this article, the authors propose a trajectory-tracking control system for tracked wall-climbing robots based on the fuzzy logic computed-torque control (FLCT) method. A key element in the proposed control strategy is to consider the adsorption force and gravity compensation based on the dynamic model. Validated via numerical simulations and experiments, the results show that the proposed controller can track the reference trajectory quickly, accurately and stably.