An　efficient　nonlinear　multigrid　method　for　a　mixed　finite　element　method　of　the　Darcy-Forchheimer　model　is　constructed　in　this　paper.　A　Peaceman-Rachford　type　iteration　is　used　as　a　smoother　to　decouple　the　nonlinearity　from　the　divergence　constraint.　The　nonlinear　equation　can　be　solved　element-wise　with　a　closed　formulae.　The　linear　saddle　point　system　for　the　constraint　is　reduced　into　a　symmetric　positive　definite　system　of　Poisson　type.　Furthermore　an　empirical　choice　of　the　parameter　used　in　the　splitting　is　proposed　and　the　resulting　multigrid　method　is　robust　to　the　so-called　Forchheimer　number　which　controls　the　strength　of　the　nonlinearity.　By　comparing　the　number　of　iterations　and　CPU　time　of　different　solvers　in　several　numerical　experiments,　our　multigrid　method　is　shown　to　convergent　with　a　rate　independent　of　the　mesh　size　and　the　Forchheimer　number　and　with　a　nearly　linear　computational　cost.