The lithium ion diffusion coefficients of bare, carbon-coated and Cr-doped $LiFePO_4$ were obtained by fitting the discharge curves of each half cell with Li metal anode. Diffusion losses at discharge curves were acquired with experiment data and fitted to equations. Theoretically fitted equations showed good agreement with experimental results. Moreover, theoretical equations are able to predict lithium diffusion coefficient and discharge curves at various discharge rates. The obtained diffusion coefficients were similar to the true diffusion coefficient of phase transformation electrodes. Lithium ion diffusion is one of main factors that determine voltage drop in a half cell with $LiFePO_4$ cathode and Li metal anode. The high diffusion coefficient of carbon-coated and Cr-doped $LiFePO_4$ resulted in better performance at the discharge process. The performance at high discharge rate was improved much as diffusion coefficient increased.