In this paper, a single-phase reactive power compensation control for static compensator (STATCOM) is developed. The primary novelty lies in that the reactive power compensation of STATCOM is reformulated as an equivalent tracking control for the reactive current, and a novel unknown system dynamics estimator (USDE) is also investigated to address the unknown system dynamics. A modeling phase based on a basic structure of single-phase STATCOM and the principle of STATCOM is first carried out to describe its behavior. To address the unknown dynamics and external disturbances, a new USDE is then developed, so that the modeling uncertainties and external disturbances can be accommodated without using a function approximator, where the demanding computational costs and tedious parameter tuning in the other control schemes are remedied. Finally, based on the proposed estimator, we design a composite control with a proportional integral (PI) feedback controller and the proposed estimator to achieve precise current tracking. The convergence analysis of both the estimation error and the control error is also given. Simulation results using a realistic simulator are presented to show the efficiency of the suggested strategy.