A finite element method is presented for the numerical simulation of time-dependent incompressible viscous free surface flows. The time-dependent primitive equations are solved sequentially using explicit time marching procedure. The method is based on a velocity correction approach to the time integration of the Navier-Stokes equations in which only the incompressibility condition is treated implicitly. A special arbitrary mixed Lagrangian-Eulerian description has been used to avoid the typical problems encountered in a purely Lagrangian description. The method appears applicable for small computers; problems requiring several thousand nodes can be solved on personal computers. Numerical experiments have been performed that show that this approach is reasonably efficient and robust for a range of complicated highly nonlinear problems.