Abstract: Based on the property of convex and compactly closed set,the author generalizes Ky Fan minimax inequality as new minimax inequality of two functions on the product space of a topological vector space and a topological space,and from this obtains a minimax inequality about one function on this product space.At the same time a section theorem is also obtained,which is the generalization of many former section theorems.It has been verified that the obtained section theorem and minimax inequality are equivalent,the former being the geometrical form of the latter.