In this paper, we study classical solution to the first initial-boundary value problem of parabolic hessian equation : where is a bounded, uniformly ( k-l )-convex domain in rn with smooth boundary 本文研究如下的拋物型hessian方程的第一初邊值問題的古典解:其中是r~n中有界一致(k-1)凸的光滑區(qū)域。