It is known that non-minimum phase zeros (NMPZ) can degrade the performance of the control systems. Especially, NMPZs bring some delays to the system making the system to be unstable in large gains. In this article, the aim is to recognize the existence of NMPZs in high voltage direct current (HVDC) lines imbedded into AC grids and to develop a method to cancel out their effects. Subsequently, the process on two real power grids with two different HVDC models are examined to detect the possible NMPZs in their dynamics. Accomplishing linear and nonlinear simulations in Matlab and Eurostag, the location of unstable zeros are determined. Then, a benchmark model is adopted to identify the affecting parameters of the power system on the occurrence of the NMPZs. The analysis concludes that the NMPZs can appear in the system as short-circuit power at connection points of HVDC line and generators. Finally, to avoid the harmful effects of theses NMPZs, a modified zero phase error compensator (MZPEC) is proposed, which is noise insensitive in the control loop. Simulation results reveal that the use of the provided MZPEC along with a classic power oscillation damping (POD) controller can greatly improve the action of the POD and, therefore, can increase the power transfer quality of the grid.