Background In order to know the multi-function changes of arable land and compare the differences of three different functional types of cities, Changsha (capital of Hunan province), Zhuzhou and Zhangjiajie are selected as research areas, representing three different functional cities as political and economic type, industrial type and tourism type, and the multi-functions of arable land in these three cities were evaluated.

Methods We constructed evaluation index system of arable land multi-functions from four aspects of production, society, culture and ecology, collected and dealt with data, analyzed the driving factors of arable land function changes in three cities using grey correlation analysis method.

Results 1) From 2007 to 2016, the productive function score of arable land in Changsha decreased from 0.271 to 0.077, then recovered to 0.274; the social function score decreased from 0.117 to 0.032; the cultural function score increased from 0.026 to 0.150; the ecological function score increased from 0.085 to 0.160. From 2007 to 2016, the productive function score of Zhuzhou arable land decreased from 0.249 to 0.126, and then increased to 0.252; the social function score decreased from 0.106 to 0.010; the cultural function score increased from 0.037 to 0.133; the ecological function score increased from 0.094 to 0.175, and then decreased to 0.040. From 2007 to 2016, the productive function score of arable land in Zhangjiajie decreased from 0.301 to 0.165, then recovered to 0.272; the social function score decreased from 0.117 to 0.056; the cultural function score increased from 0.009 to 0.106; the ecological function score decreased from 0.172 to 0.126. 2) The correlation degrees of population, urbanization rate, total fixed asset investment, total tourism income, effective irrigation area, GDP and the evolution of arable land function in Changsha were 0.805, 0.767, 0.652, 0.628, 0.601, and 0.584 respectively. The correlation degrees of effective irrigation area, number of industries above designated scale, urbanization rate, population and the evolution of arable land function in Zhuzhou were 0.824, 0.741, 0.659, and 0.632 respectively. The correlation degrees of urbanization rate, total tourism revenue, number of tourists, population, effective irrigation area, GDP and the evolution of cultivated land function in Zhangjiajie were 0.774, 0.758, 0.735, 0.716, 0.707, 0.696 respectively.

Conclusions 1) The production function of arable land in Changsha, Zhuzhou and Zhangjiajie declined first and then increased, the social function declined, the cultural function increased, and the ecological function changed differently from 2007 to 2016. 2)The driving forces of Changsha which affect the change of cultivated land function are population, urbanization rate and investment in fixed assets. 3) The driving forces of cultivated land function change in Zhuzhou are effective irrigated area, the number of industries above the scale, and urbanization rate, and those in Zhangjiajie are urbanization rate, tourism revenue, and the number of tourists. The arable land multi-function changes and its driving factors in three cities with different functions are different. The study result could provide practical basis for the cultivated land protection and the multi-functional management in different functional cities.