We introduce the Gaussian-mixture umbrella sampling method (GAMUS), a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multidimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multidimensional reaction coordinates. To illustrate GAMUS, we apply it to the alanine dipeptide (2D reaction coordinate) and tripeptide (4D reaction coordinate).