Influenza viruses are divided into three types: A, B and C. Among them, type A virus is the most virulent human pathogen and causes the most severe disease. In this paper, we propose a new time series model for influenza A virus DNA sequence, i.e.chaos game representation (CGR) radians series. The CGR coordinates are converted into a time series model, and a long-memory ARFIMA(p,d,q) model is introduced to simulate the time series model. We select randomly 10 H1N1 sequences and 10 H3N2 sequences in analysis. we find in these data a remarkably long-range correlation and fit the model reasonably by ARFIMA(p,d,q) model, and also find that we can use different ARFIMA models to identify the two kinds of sequences, i.e. ARFIMA(0,d,5) model and ARFIMA(1,d,1) model that can identify H1N1 and H3N2 respectively.