In this paper, a joint cross-layer design of adaptive modulation and coding (AMC) and cooperative automatic repeat request (C-ARQ) scheme is proposed for a secondary user in a shared-spectrum environment. First, based on the statistical descriptions of the channel, closed-form expressions of the average spectral efficiency (SE) and the average packet loss rate (PLR) are presented. Then, the cross-layer scheme is designed, with the aim of maximizing the average SE while maintaining the average PLR under a prescribed level. An optimization problem is formed, and a sub-optimal solution is found: the target packet error rates (PER) for the secondary system channels are obtained and the corresponding sub-optimal AMC rate adaptation policy is derived based on the target PERs. Finally, the average SE and the average PLR performance of the proposed scheme are presented.