In this paper, the outage performance and diversity gain of amplify-and-forward opportunistic relaying systems under the constraint of limited feedback are studied. With limited feedback, the quantization error of Channel State Information (CSI) will impact the distinguishing of the best relay and worsen the system performance. Considering this issue, the outage performance is studied and its approximate analytical expression is derived for opportunistic relaying systems with limited feedback. Further, the following two propositions are analyzed and proved: with limited feedback, no matter how many potential relays in cooperation, the diversity order can and only can be 2; with the increasing accuracy of feedback, the outage probability approaches to that of the ideal opportunistic relaying systems. Simulation results verify the analytical expression of the outage probability and the proposed propositions, which provide a theoretical support for the design of relaying protocols under the constraint of limited feedback.