Surface plasmon resonance (SPR) has been widely used as a label-free biophysical technique to quantitatively study biochemical processes. For the SPR data fitting using a single exponential function, the procedure to extract the rate constants is straightforward. However, there is no simple procedure for SPR data fitting with double exponential functions. A highly non-linear fitting procedure is, therefore, used to fit the biphasic SPR data with numerical solutions of the rate equations. This procedure requires some prior knowledge of the underlying interaction mechanism, and the extracted rate constants often have large uncertainties. In this report, we propose a new method of analyzing the biphasic SPR data using the three commonly employed biphasic models. Our method is based on a general analytical solution of the biphasic rate equations, which is much more transparent and straightforward than the highly non-linear numerical integration approach. Our method can be used to determine the underlying biphasic interaction mechanism from the analysis of the SPR data and to extract the rate constants with high confidence levels. We have illustrated the procedures with examples of the data analysis on simulated SPR profiles, and the results are discussed.