Efficient data transmission in cognitive radio networks (CRNs) is critical for cognitive radio (CR) users to communicate with each other in an opportunistic manner. Even with successful access to required channels, the transmission could still suffer from failures due to channel fading. In this paper, we propose a random linear coded scheme for efficient data transmission in multi-channel CRNs under practical fading channel conditions. We develop theoretical analysis and derive general form solutions for the batch delay associated with the proposed scheme. We also use our theoretical model to analyze the performances of two multi-channel automatic repeat request (ARQ) based schemes. Simulation results validate the analysis and show that the coded scheme outperforms the ARQ based schemes in terms of batch transmission delay. Additionally, the coded scheme is less dependent on feedback channels than the other schemes.