A gridless method for dealing with unsteady flow involving moving discrete points is investigated. The moving principle of discrete points for gridless method is proposed. The spring analogy is modified to control the movements of points caused by the motion and torsion of boundaries, so the adaptation and precision of the analogy are enhanced. The algorithm for solving Arbitrary Lagrangian-Eulerian (ALE) equations based on gridless method is accomplished. On the base of clouds in the computational region, the spatial derivatives are approximated by local least-square curve fits, HLLC (Harten, Lax, van Leer, Contact) scheme is extended into the gridless method to calculate the numerical flux and a method of flux limiter is employed in order to improve the accuracy, a multistage Runge-Kutta algorithm is used to advance the equation in time. The oscillatory pitching movement of representative airfoils is simulated, the computational results agree well with the experimental data, and the plunging movement is simulated too. It indicates that the method is successful and good at catching shock waves.