This study presents an improved compound control algorithm that substantially enhances the anti-disturbance performance of a gear-drive gyro-stabilized platform with a floating gear tension device. The tension device can provide a self-adjustable preload to eliminate the gap in the meshing process. However, the weaker gear support stiffness and more complex meshing friction are also induced by the tension device, which deteriorates the control accuracy and the ability to keep the aim point of the optical sensors isolated from the platform motion. The modeling and compensation of the induced complex nonlinearities are technically challenging, especially when base motion exists. The aim of this research is to cope with the unmeasured disturbances as well as the uncertainties caused by the base lateral motion. First, the structural properties of the gear transmission and the friction-generating mechanism are analyzed, which classify the disturbances into two categories: Time-invariant and time-varying parts. Then, a proportional-integral controller is designed to eliminate the steady-state error caused by the time-invariant disturbance. A proportional multiple-integral-based state augmented Kalman filter is proposed to estimate and compensate for the time-varying disturbance that can be approximated as a polynomial function. The effectiveness of the proposed compound algorithm is demonstrated by comparative experiments on a gear-drive pointing system with a floating gear tension device, which shows a maximum 76% improvement in stabilization precision.