Crossing moving obstacles requires different space-time adjustments compared with stationary obstacles. Our aim was to investigate gait spatial and temporal parameters in the approach and crossing phases of a moving obstacle. We hypothesized that obstacle speed affects gait parameters, which allow us to distinguish locomotor strategies. Ten young adults walked and stepped over an obstacle that crossed their way perpendicularly, under three obstacle conditions: control—stationary obstacle, slow (1.07m/s) and fast speed (1.71m/s) moving obstacles. Gait parameters were different between obstacle conditions, especially on the slow speed. In the fast condition, the participants adopted predictive strategies during the approach and crossing phases. In the slow condition, they used an anticipatory strategy in both phases. We conclude that obstacle speed affects the locomotor behavior and strategies were distinct in the obstacle avoidance phases.