Compliance control is crucial for physical human-robot interaction, which can enhance the safety and comfort of robot-assisted rehabilitation. In this study, we designed a spatiotemporal compliance control strategy for a new self-designed wearable lower limb rehabilitation robot (WLLRR), allowing the users to regulate the spatiotemporal characteristics of their motion. The high-level trajectory planner consists of a trajectory generator, an interaction torque estimator, and a gait speed adaptive regulator, which can provide spatial and temporal compliance for the WLLRR. A radial basis function neural network adaptive controller is adopted as the low-level position controller. Over-ground walking experiments with passive control, spatial compliance control, and spatiotemporal compliance control strategies were conducted on five healthy participants, respectively. The results demonstrated that the spatiotemporal compliance control strategy allows participants to adjust reference trajectory through physical human-robot interaction, and can adaptively modify gait speed according to participants' motor performance. It was found that the spatiotemporal compliance control strategy could provide greater enhancement of motor variability and reduction of interaction torque than other tested control strategies. Therefore, the spatiotemporal compliance control strategy has great potential in robot-assisted rehabilitation training and other fields involving physical human-robot interaction.