A leg-wheel robot has mechanically separated four legs and two wheels, and it performs high mobility and stability on rough terrains. In this paper, we propose gait algorithms for trot and pace gaits, and velocity limitation method, which allow continuous locomotion of a leg-wheel robot under random velocity commands. The gait algorithms which are based on the predictive event driven method determine the leg lifting timing to avoid the legs reaching the border of the work space. The velocity limitation method limits the velocity command when it exceeds the mechanical specifications of the robot. Combined the velocity limitation method with the gait algorithms, the proposed method ensures the continuity of locomotion on trot and pace gaits. It is evaluated by simulations and experiments.