We propose an mobile-to-mobile (M2M) communication system employing analog network coding (ANC) with fixed gain amplify-and-forward (AF) scheme on relay, and investigate performance of the system for the case of imperfect self-interference cancellation proceeded by the the receiver. For this purpose, first we find the expression of end-to-end signal-to-interference-noise-ratio (E2E-SINR) at the receiver. Then, we derive the closed form expression of the cumulative density function (CDF) of E2E-SINR for the fast fading cascaded Rayleigh channel conditions. Using this CDF, we obtain the closed-form expression of outage probability. Finally, we verify the analytic results by comparing with computer simulations. Our results show that the outage probability increases when the success of the self-interference cancellation by the receiver decreases. Also it is shown that the increasing cascading degree of the channels decreases the outage performance of the system.