Deriving the quenching phenomena to an initial-boundary value problem in a bounded domain in the Rⁿ for the mean curvature equation with a nonlinear convection term:u_t-div[σ(¨u²)¨u]+b(u)·¨u=0.If u₀∈L^q,q≥n,the solution will quench in limit time.We also give the L^∞-estimate.