Accurate estimation of the state of charge (SOC) and state of health (SOH) is crucial for the safe and reliable operation of batteries. However, the measurement bias of voltage can highly deteriorate the estimation accuracy. One such example is the lithium iron phosphate (LFP) battery, which is highly prone to suffer from this issue owing to its flat open-circuit voltage curve. This work proposes a bias-compensated framework that reliably estimates the SOC and SOH of LFP batteries under the influence of voltage measurement bias. To validate the proposed approach, four LFP batteries are tested at various ambient temperatures and SOH conditions, with two different values of voltage measurement bias added. The results show that the bias-compensated algorithm achieves test errors that are less than 1.5% and 2% for SOC and SOH estimation, respectively. Additionally, the proposed approach outperforms the traditional estimation method that ignores the effects of voltage measurement bias.