Abstract: An efficient algorithm is devised and analyzed for Two-Dimension Heat-conduction equation. It is proved that the ETF-FDS-MG(Extended Trapezoidal Formula Finite Difference Scheme Multigrid) method is third-order in time, two-order in space, unconditionally stable and high order convergent. Numerical example confirms the ETF-FDS-MG method is superior to the FE-MG(Finite Element Multigrid) method.