In this study, we introduce the concept of P-3-prime ideal for an ideal P of a near-ring. Then, the relations between P-3-prime ideal and P-c-prime ideal are obtained. It is proved that a P-c-prime ideal is a P-3-prime ideal. But, in general, the converse relation does not hold. However we provide some additional conditions for the converse to be true. We provide examples to illustrate our results. Finally, some results about P-identity and P-inverse are also observed.