In this paper, we consider an incremental relaying protocol based on an amplify-and-forward transmission in conjunction with a best relay selection scheme over non-identically distributed relay channels. In order to satisfy the spectral efficiency and the bit error rate (BER) requirements, adaptive modulation is applied to our proposed scheme. We derive the average spectral efficiency, average BER and outage probability for the performance analysis of our proposed scheme. For a more tractable analysis, we start with an upper bound for the combined signal-to-noise ratio at the destination and provide closed-form expressions for independent non-identically distributed Rayleigh fading conditions. Our analytical-based numerical results are validated by some computer-based simulations. These results show that our proposed scheme leads to a considerable improvement in the performance of cooperative diversity systems.