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In this paper, we introduce the opportunistic nonorthogonal amplify-and-forward (NAF) single-antenna cooperative system with blind relays over Rayleigh fading channel and the optimal power allocation is studied for this scheme. The optimal power allocation for NAF system is carried out with three steps based on the opportunistic relay selection (ORS) and its formulation is obtained to maximize the system capacity. With the help of extreme value algorithm, the power allocation factor can be assigned for the source and the selected relay node with a simple method. Simulation results show that the performance of the proposed optimal power allocation scheme outperforms the equal power allocation scheme and direct transmission as well as the orthogonal amplify-and-forward (OAF) scheme.