We propose a cross-layer design combining adaptive modulation and coding (AMC) at the physical layer with a hybrid automatic repeat request (HARQ) protocol at the data link layer in multi-relay networks with imperfect channel state information (CSI). Based on a simple and distributed relay selection strategy, we derive the closed-form expressions for performance metrics such as average packet loss rate (PER) and spectral efficiency; and further formulate an optimization model to maximize the spectral efficiency under the target PER constraint. The numerical results show that the average PER is lower and the spectral efficiency is higher with the number of the relay increasing.