With the rapid development of social economy in Chengdu, it is of great significance to analyze the accessibility of a public facilities resources, and services in respective regions for the spatial planning of public facilities and the optimization of urban construction in Chengdu. Most existing studies only consider the accessibility of a single public facility under a single transportation mode studying facilities at the same level. In this research, with the consideration of all these factors mentioned above, an improved 3‐step floating catchment area (3SFCA) model of multi‐transportation modes is introduced to analyze the accessibility and spatial distribution of multiple types of public facilities under multiple traffic modes. The new model classifies the grade of public facilities and calculates the service accessibility of public facilities under the driving, public transport, cycling, and walking modes in the five dimensions of education, medical care, commerce, transportation, and leisure in the central urban areas of Chengdu. Through the comparative analysis of multiple models, we found that the improved 3SFCA can more accurately evaluate the accessibility of all dimensions of public facilities in central urban areas of Chengdu. The accessibility of compound public facilities in the central city is excellent. With the gradual expansion to the outward areas, the diversity and accessibility of compound public facilities gradually decreases. Furthermore, the accessibility distribution of public facilities in the study area is not balanced. The accessibility between the central urban areas and the marginal areas differs greatly and the spatial differentiation is substantial.