The density function of Student's t random variable with n degrees of freedom, f_n(t), can be approximated by a finite mixture density function from the same distribution. The criteria of approximation is to minimize the difference between the moments of f_n(t) and that of its finite mixture approximation. The proposed approximation may be applied to obtain an explicit and simple form for the characteristic function of Student's t distribution of even number of n. It is evaluated for different values of n, and good results can be obtained even when n is as small as 5.