This paper presents a method for constructing multiple- valued switching functions based on Galois fields. First the constructing Inethod for single- variable switching functions is developers and the results are extended to multiple- variable functions. The fundalnental Inathelnatical properties used in this paper are. (1) The sum of all elements over CF of is zero. (2) The Product of nonzero elements over GF(N) is equal to e1 for Neven, and e1( ) for N odd. With these properties, a relatlvely simple constructing method is developed, and a process for determining the coefficients of the expanded forms of switching functions is also obtained without successive multiplication of the polynomials. Some examples are given to illustrate the method.