In this paper, the possible value of the differential uniformity of a function over finite fields is discussed. It is proved that, the differential uniformity of a function over Fq can be any even integer between 2 and q when q is even; and it can be any integer between 1 and q except q-1 when q is odd. Moreover, for any possible differential uniformity t, an explicit construction of a differentially t-uniform function is given.
