Although there already exists a rich literature on cooperative diversity, current results are mainly restricted to the conventional assumption of additive white Gaussian noise (AWGN). AWGN model realistically represents the thermal noise at the receiver, but ignores the impulsive nature of atmospheric noise, electromagnetic interference, or man-made noise which might be dominant in many practical applications. In this paper, we investigate the performance of cooperative communication over Rayleigh fading channels in the presence of impulsive noise modeled by Middleton Class A noise. Specifically, we consider a multi-relay network with amplify-and-forward relaying. Through the derivations of the pairwise error probability, we quantify the diversity advantages. Based on the minimization of a union bound on the error rate performance, we formulate optimal power allocation schemes and demonstrate significant performance gains over their counterparts with equal power allocation. An extensive Monte Carlo simulation is also presented to illustrate the performance of cooperative schemes in various impulsive environments.