Technical challenges facing determination of battery available power arise from its complicated nonlinear dynamics, input and output constraints, and inaccessible internal states. Available solutions often resorted to open-loop prediction with simplified battery models or linear control algorithms. To resolve these challenges simultaneously, this paper formulates an economic nonlinear model predictive control to forecast a battery's state-of-power. This algorithm is built upon a high-fidelity model that captures nonlinear coupled electrical and thermal dynamics of a lithium-ion battery. Constraints imposed on current, voltage, temperature, and state-of-charge are then taken into account in a systematic fashion. Illustrative results from several different tests over a wide range of conditions demonstrate that the proposed approach is capable of accurately predicting the power capability with the error less than 0.2% while protecting the battery from undesirable reactions. Furthermore, the effects of temperature constraints, prediction horizon, and model accuracy are quantitatively examined. The proposed power prediction algorithm is general and then can be equally applicable to different lithium-ion batteries and cell chemistries where proper mathematical models exist.