The existence and uniqueness of generalized solution to the first bound-ary value problem for parabolic Monge-Ampère equation-ut det D2xu= f in Q =Ω×(0, T], u = ψ on δpQ are proved if there exists a strict generalized supersolution uψ,where Ω Rn is a bounded convex set, f is a nonnegative bounded measurable func-tion defined on Q, ψ ∈ C( pQ), ψ(x, 0) is a convex function in Ω-, x0 ∈ Ω, ψ(x0, t) ∈Ca([0, T]).