Lack of parking spaces at downtown hospitals causes urban problems like patient access delays and additional carbon emissions. This paper proposes a cumulative prospect theory-based shared parking space allocation model (CPT-SPSA model) to alleviate the parking difficulties. The CPT-SPSA model aims to maximize the profit of the shared parking platform under time window constraints considering the parking choice behavior of hospital parkers. To determine the parking choice behavior, cumulative prospect theory (CPT) is utilized to model parkers' evaluation of parking lots considering individual heterogeneity. Numerical experiments indicate that the profit of the platform and the utilization rate of the shared parking spaces are improved significantly and more successful matches of shared parking supply and demand are achieved under the CPT-SPSA model. Those with different parking purposes vary in acceptance of each parking lot. The platform can earn more profit by reasonably adjusting the parking fees of the shared parking spaces.