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This paper introduces a simple and fast lossless compression algorithm, called CAD, for the compression of protein sequences. The proposed algorithm is specially suited for compressing proteomes, which are the collection of all proteins expressed by an organism. Maintaining a changing dictionary of actively used aminoacid residues, the algorithm uses the adaptive dictionary together with Huffman coding to achieve an average compression rate of 3.25 bits per symbol, better than most other existing protein-compression and generalpurpose compression algorithms known to us. With an average compression ratio of 2.46: 1 and an average compression rate of 1.32 M residues/sec, our algorithm outperforms every other compression algorithm for compressing protein sequences in terms of the balance in compression-time and compression rate.