Numerical simulation of acoustic-shock waves interaction in quasi-one dimensional convergent-divergent nozzles is performed. The time dependent nature of flow field is initiated by using very small amplitude acoustic wave that incident on the inlet of the nozzle. Computations are performed using 3-point fourth-order compact implicit McCormick-type scheme to approximate the spatial derivatives and the two steps 5-6 alternating 2-N storage Low-Dispersion and —Dissipation Runge-Kutta (LDDRK) method as a time marching scheme. Artificial damping terms were used in damping non-physical very high wave numbers waves. The obtained numerical solutions with acoustic perturbation are presented.