Considering the speed regulation problem of converter-driven motor systems (CDMS), a composite finite-time anti-disturbance control scheme is proposed in this paper. Firstly, the controller design process is mainly divided into two blocks according to block backstepping control techniques. Then, by constructing universal finite-time observers (UFTO), immeasurable system dynamics and multiple disturbances are estimated, simultaneously. Based on the estimated information, the integral terminal sliding mode control (ITSMC) strategies devised for the CDMS exhibit robust disturbance rejection capabilities. Compared with existing methods, the proposed composite control scheme is distinguished by its reliance solely on measured output, enhanced dynamic response speed, superior disturbance rejection capability, and a more streamlined controller design. Furthermore, a rigorous global finite-time stability analysis is presented for the closed-loop system. Finally, numerous experimental results are given to validate the effectiveness of the proposed control scheme.