The boundary value problem of a kind of quasi-linear parabolic equations is discussed. , Ω={(x, t) | 0 < x < l, - ∞ < t < + ∞}.This paper firstly introduces H ö lder space (Ω) of T-periodic continuous function and following function: F(x, t, w)= . The time periodic solution u(x, t) which satisfied j(x)≤u(x, t)≤j(x)is obtained under some assumed conditions of known functions, by use of method upper and lower solution and Leray –Schauder fixed-point theorem to following boundary value problem . The existence of time periodic solution to boundary value problem is proved by the definition of the function F.