We propose an integer chaos game representation (iCGR) of DNA sequences and a lossless encoding scheme for DNA sequences by iCGR. In the iCGR method, a DNA sequence is represented by the iterated function of the nucleotides and their positions in the sequence. Then the DNA sequence can be uniquely encoded and recovered using three integers from iCGR. One integer is the sequence length and the other two integers represent the accumulated distributions of nucleotides in the sequence. The encoding scheme for DNA sequences by iCGR is one-to-one loseless. The three integers contain all the sequence information. Therefore, the original DNA sequence can be decoded from the three encoded integers.