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Using a moving-mesh, nonhydrostatic, spectral element model, we simulate Langmuir circulation with Navier-Stokes equations under explicit, freely propagating surface waves. For comparison, Langmuir circulation is also simulated with Craik-Leibovich (C-L) equations. In both simulations, the Langmuir circulations are very similar, including temporal formation progresses and spatial structures; however, the strength of Langmuir circulation in the C-L simulation is a bit weaker, which we suggest is due to the lack of Eulerian mean drift induced by fluid viscosity in the presence of explicit surface waves.