In the case of images captured by color filter array (CFA), the compression-first approach (compression of CFA) is shown to be better than the demosaick-first approach (general image compression). In this paper, we propose a new H.264/AVC based compression-first approach that exploits the correlation between the color channels. For this, we propose an inter-channel prediction model described by a linear equation in the RGB space. Specfically, the R and B pixels are predicted by a neighboring G pixel or demosaicked G pixel at the same location. The proposed prediction scheme further reduces the variance of prediction error, and as a result the proposed method provides about 1.45dB gain on average and 2.2dB gain at maximum for the green channel over the conventional compression-frist scheme. For the non-green channel, average gain is about 1.0dB and maximum gain is about 1.8dB.