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Both the KdV solitary waves and the envelope solitary waves in dusty plasma have been proposed by using the reductive perturbation method.It is verified by using the particle-in-cell(PIC)numerical method.There is no phase shift after the head on collision between two envelope solitary waves,while there are phase shifts of two colliding KdV solitary waves after head on collision.Head-on collision and overtaking collision between a KdV solitary wave and an envelope solitary wave are studied by using Particle-in-cell(PIC)method in a dusty plasma.Furthermore,the rogue wave solution can be obtained from the Nonlinear Schrodinger Equation(NLSE)which can be obtained from the fluid dynamical equation of dusty plasma.