Low-frequency response, strong nonlinearity and unknown disturbances are the main challenges faced by the engineering application of the pump-controlled electro-hydraulic steering systems (EHSSs) for heavy vehicles. To solve the above problems, an active disturbance suppression controller is proposed based on a variable rate reaching law (VRRL) and a terminal sliding mode observer (TSMO) in the framework of the sliding mode control. This controller is unique because, the VRRL introduces a nonlinear activation function, which enables smooth switching between multiple reaching rates, effectively improving the response speed and the disturbance rejection performance of the pump-controlled EHSS. Furthermore, an adaptive incomplete disturbance compensation control strategy is proposed by incorporating a TSMO to further improve the accuracy and robustness of the steering system, which employs a VRRL-based TSMO to realize accurate estimation of the lumped disturbance in finite time, and avoids controller overcompensation by selecting a preferred disturbance compensation coefficient. The stability analysis demonstrates that the proposed controller effectively suppresses the lumped disturbance and reduces the convergence domain of the steering system. A pump-controlled EHSS experimental bench is constructed, and a series of experiments are conducted with various steering frequencies and load conditions, which validate the ability of the proposed controller to achieve high-precision dynamic steering in all-terrain conditions of the pump-controlled EHSS for heavy vehicles.