In order to achieve the normal walking of hemiplegic patients, this paper proposes a single-legged exoskeleton robot according to the bionics principle, and presents an adaptive adjustment strategy for walking characteristics. The least square regression analysis is used to fit the angle data of healthy leg joints by cubic polynomials, and then the parametric design of the fitted curve is carried out to obtain the influence of the user’s stride frequency and stride length on the joint angle, so that the gait of the exoskeleton can be adjusted in real time according to the stride length and stride frequency of the healthy leg to realize normal walking. In order to verify the effectiveness of the adaptive adjustment strategy proposed in this paper, the angle of leg joints under normal gait is collected in advance. In addition, an adult male is chosen as the subject to walk on the horizontal ground wearing the single-legged exoskeleton as the experiment. The experimental results show that the designed exoskeleton is reasonable, and the adaptive adjustment strategy proposed in this paper can make the exoskeleton adapt well and follow the gait of healthy legs to achieve a more natural walking state.