In order to realize stable control of the underactuated biped robot on varying height steps with a known step height, a stable walking control strategy based on the adaptive feedforward control algorithm is proposed. Firstly, considering the ground deformation, pairs of spring-damper units are employed to model the ground, and a "robot-step" coupling dynamic model is established. Secondly, the "multiple-input-multiple-output" model of "robot-step" is simplified to the "single-input-single-output" model consisting of centroid displacement and velocity. Then varying height steps are equivalent to varying slopes, whose equivalent slope angle and the desired step length for each step can be calculated according to the each step height. An adaptive control coefficient is introduced into the control algorithm, and it is adjusted according to the equivalent slope angle to track the reference velocity of the CoM (center of mass). Finally, simulation experiments are conducted to validate the proposed controller in the environment where the varying height of the step is less than 0.032 m. The simulation results demonstrate that stable walking can be achieved on varying height steps with a known step height by implementing the proposed control strategy.