A wireless-powered sensor network (WPSN) consisting of one hybrid access point (HAP), a near cluster and the corresponding far cluster is investigated in this paper. These sensors are wireless-powered and they transmit information by consuming the harvested energy from signal ejected by the HAP. Sensors are able to harvest energy as well as store the harvested energy. We propose that if sensors in near cluster do not have their own information to transmit, acting as relays, they can help the sensors in a far cluster to forward information to the HAP in an amplify-and-forward (AF) manner. We use a finite Markov chain to model the dynamic variation process of the relay battery, and give a general analyzing model for WPSN with cluster cooperation. Though the model, we deduce the closed-form expression for the outage probability as the metric of this network. Finally, simulation results validate the start point of designing this paper and correctness of theoretical analysis and show how parameters have an effect on system performance. Moreover, it is also known that the outage probability of sensors in far cluster can be drastically reduced without sacrificing the performance of sensors in near cluster if the transmit power of HAP is fairly high. Furthermore, in the aspect of outage performance of far cluster, the proposed scheme significantly outperforms the direct transmission scheme without cooperation.