As part of urban green space and emergency shelters, refuge green spaces (RGS) contribute significantly to the resilience of cities to natural disasters. In contrast, few studies have been conducted to assess the equity of RGS in relation to their planning layout. The presented research aims to quantitatively evaluate the equity of RGS within Chengdu’s Third Ring Road, and to propose corresponding optimization measures in conjunction with future green space planning. The rapid evacuation capacity of the RGS was evaluated by calculating the equity of the RGS in walking modes of 5, 10 and 15 min using an improved three-step floating catchment area method (3SFCA). Based on the results, RGS had an average equity in the study area. The total number of RGS within the Third Ring Road of Chengdu was insufficient, with an uneven spatial distribution and a structure to be optimized. The rapid evacuation capacity of RGS in 5 and 10 min needs to be further improved. The short-term resettlement capacity of RGS after 15 min was relatively good. Using Moran’s I index, the RGS equity and house price results were analyzed and no significant aggregation and polarization were observed. Following the evaluation, recommendations are made for optimizing and adding future RGS in accordance with Chengdu Green Space System Planning. The equity of RGS has been significantly improved after optimization, which can meet the needs of over 90% of residents for 15 min. This study provided feasible suggestions for the layout and structural optimization of the future RGS within the Third Ring Road of Chengdu, which aimed to create a RGS network with complex functions, to meet the multiple needs of citizens.