This paper investigates the outage probability of an energy harvesting (EH) relay-aided cooperative network, where a source node transmits information to its destination node with the help of an energy harvesting cooperative node. For such a system, we derive an explicit closed-form expression of outage probability over Nakagami-m fading channels for both amplify-and-forward (AF) and decode-and-forward (DF) relay protocols, and we verify the explicit closed-form expressions of outage probability with the Monte Carlo method. It is shown that the simulation results match well with the numerical ones. From the numerical analysis and simulation results, it can be observed that the system parameters have great impact on both AF and DF relay systems. For the DF system, with the increment of the power splitting ratio, the system outage probability decreases, while for the AF system, with the increment of the power splitting ratio, it first increases and then decreases. Besides, for both DF and AF systems, when the relay is placed relatively closer to the source, better outage performance will be achieved.