A meshless local Petrov-Galerkin (MLPG) method basing on the moving Kriging interpolation is employed for solving two-dimensional structural dynamic problems, in which the Heaviside step function is used as the test function in each sub-domain and the precise time step integration method is selected for the time discretization scheme. The essential boundary conditions can be implemented directly as the shape functions possess the Kronecker Delta property. This method does not involve the sub-domain and singularity integral in generating the global stiffness matrix except for the boundary integral. Numerical examples have shown that the MLPG method basing on the moving Kriging interpolation has the advantage of easy implementation and high accuracy.