This study addresses the robust distributed relay network (DRN) beamforming design problems for a distributed Amplify-and-Forward (AF) relay aided multiuser peer-to-peer communication system in the presence of imperfect channel state information (CSI). By adopting a stochastic CSI error model, two robust optimal design problems are considered. One is aimed at balancing the signal-to-interference plus noise ratio (SINR) at destinations under the DRN total transmit power constraint concerning the fairness, the other is to minimize the DRN total transmit power with the guarantee of QoS requirements (SINRs exceed preassign thresholds) at destinations concerning the efficiency. The analysis and modeling indicates that the problems above are the intractable problems. By introducing the semidefinite relaxation (SDR) technique, the intractable problems hereinbefore can be converted into the semidefinite program (SDP) problems which can be solved efficiently through the interior-point method. The robust performance of the proposed designs is demonstrated through simulations. 