A nanosized LiFePO4/C composite with a complete and thin carbon-shell is synthesized via a ball-milling route followed by solid-state reaction using poly(vinvl alcohol) as carbon source. The LiFePO4/C nanocomposite delivers discharge capacities of 159, 141, 124 and 112 mAh g(-1) at 1 C, 5 C, 15 C and 20 C, respectively. Even at a charge-discharge rate of 30 C, there is still a high discharge capacity of 107 mAh g(-1) and almost no capacity fading after 1000 cycles. Based on the analysis of cyclic voltammograms, the apparent diffusion coefficients of Li ions in the composite are in the region of 2.42 x 10(-11) cm(2) s(-1) and 2.80 x 10(-11) cm(2) s(-1). Electrochemical impedance spectroscopy and galvanostatic intermittent titration technique are also used to calculate the diffusion coefficients of Li ions in the LiFePO4/C electrode, they are in the range of 10(-11)-10(-14) cm(2) s(-1). addition, at -20 degrees C. it can still deliver a discharge capacity of 122 mAh g(-1), 90 mAh g(-1) and 80 mAh g(-1) at the charge-discharge rates of 0.1 C. 0.5 C and 1 C, respectively. (C) 2011 Elsevier B.V. All rights reserved.