Land-use zoning provides an effective tool for designing and implementing differentiated farmland-protection policies. Despite the exponential increase in research on farmland zoning in recent years, little research has comprehensively explored the supply, demand and relationships of the diverse functions of farmland. In this study, multi-sourced datasets and diverse methods, along with GIS, were combined to spatially evaluate the supply, demand and relationship patterns among the production, ecological and landscape-cultural functions of the farmland of Hangzhou City in China, to construct farmland zoning. The results indicate that high production supply was mostly concentrated in flat plains, whereas highly ecological farmland was frequently observed in mountains. Both urban and rural areas had the capacity to provide aesthetics and recreation. Regarding demand, high values were mainly observed near the downtown area. Additionally, supply-and-demand matching (SDM) and multi-functional coupling and coordination degree (MCCD) were evaluated. Among the four basic zones acquired by SDM analysis, two zones dominated by more than one function were further divided into four sub-regions, according to the MCCD values. Ultimately, six farmland-use zones were determined. By considering the supply, demand and relationships of multiple functions, this farmland-zoning program offers new insights into differentiated farmland protection.