The present disclosure discloses a method and apparatus for controlling robot motion, a device and a storage medium, which belongs to the field of robot motion control technologies. The method includes: determining a remaining duration of a current stepping cycle, wherein the remaining duration is a duration from a current moment to an end moment of the current stepping cycle; predicting, based on the remaining duration, an expected velocity of a robot, a first center of mass position and a first instantaneous velocity of the robot at the current moment, and a state space equation, a second center of mass position and a second instantaneous velocity of the robot at the end moment of the current stepping cycle; determining, based on the expected velocity, the second center of mass position and the second instantaneous velocity, a stable foothold position corresponding to the current stepping cycle; determining, based on the stable foothold position and the second center of mass position, a motion parameter corresponding to each joint in the robot associated with stepping; and controlling the robot based on the motion parameter corresponding to each joint. By means of the solution, it is beneficial to improve the stability of the robot during the motion.