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The urban park is the main leisure and entertainment place in residents’ daily lives. The accessibility of parks is closely related to the physical and mental health of the residents. Although many scholars have conducted a great deal of research on the spatial accessibility of urban parks, they have rarely considered the supply competition among different parks and the impact of multiple travel modes on the spatial accessibility of parks. Therefore, based on Baidu map navigation data, in this paper, the park Baidu score is used to represent the competitive relationship among different parks, and the impact of multiple travel modes on the spatial accessibility of parks is considered. A supply competition and multiple travel modes Gaussian two-step floating catchment area (SCM-G2SFCA) model is established to evaluate the spatial accessibility of the parks in the Wuhou District, Chengdu, China. The results show that (1) compared with traditional methods, the SCM-G2SFCA model can obtain more accurate results using Baidu map navigation data. (2) There are obvious spatial differences in the accessibility distribution of the parks in the Wuhou District, Chengdu, with high accessibility in the south and low accessibility in the north. The Jinyang and Huaxing sub-districts in the southern suburbs have the highest park accessibility and can obtain more adequate park services. The Fangcaojie and Cujin sub-districts in the northern urban areas have the lowest park accessibility and are relatively lacking in park services. The research results of this study have important reference value for the rational planning of urban parks and the improvement of the spatial accessibility of urban parks in the Wuhou District of Chengdu and similar urban areas. Full article