This article develops a high-precision tracking control without velocity measurement for electro-hydraulic actuators subject to mismatched and matched disturbances. Compared with previous studies, the presented control method is attractive from a practical point of view. First, velocity signal is often approximately derived by numerical differentiation on position signal, nevertheless, accompanied heavy noise will severely deteriorate tracking performance. Thus, to avert using noise-polluted velocity signal, a third-order super-twisting algorithm (STA) is developed to achieve velocity estimation. Second, the STA-based disturbance estimator is employed to estimate and compensate mismatched and matched disturbances in finite time. Then a composite STA-based control law is constructed to achieve a velocity-free high-performance tracking control, in which an employed modified STA only with an adjustable gain is easier to be performed for practical implementation. The stability analysis reveals the proposed controller is asymptotically stable while existing time-variant disturbances. Comparative experiment results validate the superiority of the presented method.