This paper studies the outage performance of a cognitive Amplify-and-forward(AF) relay network subject to Rayleigh fading.Under the condition of imperfect Channel state information(CSI) estimations of the links from the secondary system to the Primary user(PU),the closed-form upper and lower bounds of the outage probability are derived through a geometrical analysis method.An asymptotic analysis of the outage probability is also derived in the high Signal-to-noise ratio(SNR)regime to gain additional insights on the system.The simulation results corroborate our theoretical analysis,and the effectiveness of the geometrical analysis method is verified with the conventional approach as a benchmark.The asymptotic results are very tight with the analytical lower bound in the high SNR regime.It also can be observed from the simulation results that the impact of the number of relays as well as the imperfect CSI on the outage probability and the diversity order. This paper studies the outage performance of a cognitive Amplify-and-forward (AF) relay network subject to Rayleigh fading. Undertaking conditions of imperfect Channel state information (CSI) estimations of the links from the secondary system to the Primary user (PU) , the closed-form upper and lower bounds of the outage probability are derived through a geometrical analysis method. An asymptotic analysis of the outage probability is also derived in the high Signal-to-noise ratio (SNR) regime to gain additional insights on the system. The simulation results corroborate our theoretical analysis, and the effectiveness of the geometrical analysis method is verified with the conventional approach as a benchmark. asymptotic results are very tight with the analytical lower bound in the high SNR regime. from the simulation results that the impact of the number of relays as well as the imperfect CSI on the outage probability and the diversity order.