The author presents an adaptive multigrid method for solving the stationary Navier-Stokes equations. The so-called tri-tree algorithm is used in order to construct a hierarchical grid. Then at each level the Navier-Stokes equations are solved approximately with the help of Newton's method. The (suitably projected) solution from the level above is chosen as a start vector which guarantees that only a few linear iterations are necessary. Numerical results are given for the cavity problem, and the number of iterations is compared to the corresponding numbers for two other methods.