We investigate a wireless-powered cooperative relay network, where an energy constrained relay node accumulates the energy harvested from radio frequency signals, and then assists source signal transmission. An adaptive cooperative transmission scheme for cooperative relay network is developed. The relay helps to transmit the source signal only if it has harvested enough energy and the channels between source and relay do not suffer from an outage. Before each transmission block, one out of two transmission modes, i.e., Half-duplex (HD) or Full-duplex (FD), is dynamically adopted based on the maximal instantaneous capacity of the system. A closed-form expression for the exact outage probability of the system with the proposed scheme is derived. Monte Carlo simulations are run to validate the accuracy of the mathematical analysis, and numerical results show that the proposed protocol outperforms the existing fixed cooperative transmission modes.