Though it becomes a routine to fit impedance data to an equivalent electric circuit model (EECM) using complex nonlinear least square (CNLS) to extract physical parameters from impedance data, two formidable challenges still remain: to build a physically meaningful EECM and to find good initial estimates for model parameters. In this study, combining graphical analysis of impedance data in both Bode and Nyquist plots, a two-step procedure is proposed to address the challenges: (1) a frequency derivative phase angle method is developed in Bode plot to identify the number of time constants (or electrochemical processes); (2) graphical analysis of impedance data in Nyquist plot is used sequentially for initial parameter determination. Major graphical analysis methods are compared in terms of frequency resolution, accuracy and complexity using synthetic data. The superiority of the proposed procedure is illustrated using the experimental data of a three-electrode lithium-ion cell.