In multidimensional fluid dynamics, methods based on mesh meet difficulties frequently, especially in problems with multimaterial media and large deformation grids.In this paper, a new meshless Lagrangian finite point method to compute unsteady compressible flows is presented. In this method discrete points are distributed in the physical domain, and are regarded as Lagrangian points with mass, velocity and energy. At a given point, a "cloud" of points in the vicinity are chosen and the relations between them are set. The Lagrangian fluid equations other than the SPH ones are discreted with the Godunov method in which the interface is in a position of connect line between the given point and its neighbors. To enhance robustness and accuracy of the algorithm, more neighbor cloud points are introduced and the least square approximation is facilitated in the simulation. Computed results are good for classical examples.