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The equity of transport accessibility is a prerequisite for sustainable development targets, especially in the ecologically fragile area of the Tibetan Plateau (also known as the Qinghai-Tibet Plateau). The relationship between transportation supply and social demand has become a key element of socioeconomic development and environmental protection in agricultural and pastoral areas. Based on data from transportation networks, permanent populations and the economy, this study uses a network analysis model, the coefficient of variation and the Gini coefficient to construct an index of social demand in townships and analyse the equity of transport accessibility on the Tibetan Plateau between 1980 and 2017; the principle of geographic distribution and the spatial relationship between transport accessibility and social demand at the township scale are also discussed. This study finds the following: the development of transportation has improved accessibility on the Tibetan Plateau, creating a highly accessible region with important cities as the nodes and major traffic arteries as the axes; both the coefficient of variation of transport accessibility and the Gini coefficient have increased slightly; and the equity of transport accessibility among townships on the Tibetan Plateau has exhibited a downward trend. Further, the social demand index is doubling every ten years, the spatial distribution has regional characteristics, and a decrease in permanent populations is the main reason for declining social demand index scores among townships. Townships with the lowest and highest social demand index scores for transportation development enjoy greater transportation benefits; there is a significant spatial relationship between social demand and location conditions (potential accessibility); the aggregation of social demand and accessibility types follows specific geographical distribution principles; and the Mangya-Gongshan Line delineates the distribution characteristics of township clusters with low social demand and low accessibility.