We study the function spaces on local fields in this paper, such as Triebel Btype and F-type spaces, Holder type spaces, Sobolev type spaces, and so on, moreover,study the relationship between the p-type derivatives and the Holder type spaces. Our obtained results show that there exists quite difference between the functions defined on Euclidean spaces and local fields, respectively. Furthermore, many properties of functions defined on local fields motivate the new idea of solving some important topics on fractal analysis.