The next-generation 5G networks will integrate two technologies, cognitive radio and cooperative communication, which use radio spectrum opportunistically and efficiently, in addition, they enhance the reliability and the capacity of the system. In this paper, we present a novel power control scheme based on a relaxed constraint at cognitive relay network under both the outage probability limit (OPL) of the primary system and the interference constraint limit (ICL). We show how to transform the optimization problem of the condition on the OPL and the ICL into a condition on the channel, so that the cognitive user observes the channel from cognitive source to primary receiver, and control its transmit power based on the channel condition. We derive the closed-form expressions of the outage probabilities over independent but not necessarily identically distributed Nakagami-m fading channels. By using the theoretical analysis and from the numerical results, firstly, we show that the proposed power control scheme which based on both the OPL and the ICL achieves better performance in underlay spectrum rather than the traditional which based only on the interference constraints. Secondary, we show that the proposed scheme allows lower power consumption at cognitive side while the performance of cognitive relay network is improved and the QoS of primary system is guaranteed in parallel.Index Terms-Cognitive relay network, interference constraint limit, outage probability limit, spectrum underlay, power control, Nakagami-m Fading.