In this paper an efficient mesh-moving Finite Element model for the simulation of the incompressible flow problems is proposed. The model is based on a combination of the explicit multi-step scheme (Runge–Kutta) with an implicit treatment of the pressure. The pressure is decoupled from the velocity and is solved for only once per time step minimizing the computational cost of the implicit step. Novel solution algorithm alleviating time step restrictions faced by the majority of the former Lagrangian approaches is presented. The method is examined with respect to its space and time accuracy as well as the computational cost. Two numerical examples are solved: one involving a problem on a domain with fixed boundaries and the other one dealing with a free surface flow. It is shown that the method can be easily parallelized.