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In this article, we study the homogenization of the nonlinear degenerate parabolic equation $$ partial_t b({x /varepsilon},u_varepsilon) - mathop{ m div} a({x /varepsilon},{t /varepsilon}, u_varepsilon,abla u_varepsilon)=f(x,t), $$ with mixed boundary conditions(Neumann and Dirichlet) and obtain the limit equation as $varepsilon o 0$. We also prove corrector results to improve the weak convergence of $abla u_varepsilon$ to strong convergence.