Abstract The battery state of available power (SOAP) is crucial to improve the energy management of electric vehicles (EVs) and protect batteries from damage. This paper proposes a novel supervisory long-term prediction scheme of SOAP for lithium-ion batteries in electric vehicles. The supervisory long-term prediction denotes that the SOAP is online predicted under the supervision of the EV’s future long-term driving conditions, instead of the traditional approaches under the constant working limitations. Firstly, to accurately capture the battery dynamics, a battery model incorporated with multi-parameters dynamic open circuit voltage is established, and the least square approach with an adaptive forgetting factor is applied to online identify the battery parameters. A new battery state estimation algorithm based on an adaptive two step filter is then proposed to improve the accuracy of the state estimation. A battery’s long-term power demand (LTPD) prediction model is also established for EVs. Based on the improved battery model and predicted battery states, especially under the supervision of the predicted LTPD, the novel supervisory long-term battery SOAP prediction approach is finally put forward to make the prediction practical and accurate. The long-term state of charge (SOC) and SOAP of battery are online co-predicted by the derived algorithms. The robustness of the proposed approach against erroneous initial values, different battery aging levels and ambient temperatures is systematically evaluated by experiments. The experimental results verify the long-term battery SOAP prediction error reduced by 85.9% when compared with that by traditional approaches.