In this paper, we investigate power allocation scheme and outage performance for a physical-layer network coding (PNC) relay based secondary user (SU) communication in cognitive multi-antenna relay networks (CMRNs), in which two secondary transceivers exchange their information via a multi-antenna relay using PNC protocol. We propose an optimal energy-efficient power allocation (OE-PA) scheme to minimize total energy consumption per bit under the sum rate constraint and interference power threshold (IPT) constraints. A closed-form solution for optimal allocation of transmit power among the SU nodes, as well as the outage probability of the cognitive relay system, are then derived analytically and confirmed by numerical results. Numerical simulations demonstrate the PNC protocol has superiority in energy efficiency performance over conventional direct transmission protocol and Four-Time-Slot (4TS) Decode-and-Forward (DF) relay protocol, and the proposed system has the optimal outage performance when the relay is located at the center of two secondary transceivers.