This paper presents a new overall system for state-of-available-power (SoAP) prediction for a lithium-ion battery pack. The essential part of this method is based on an adaptive network architecture which utilizes both fuzzy model (FIS) and artificial neural network (ANN) into the framework of adaptive neuro-fuzzy inference system (ANFIS). While battery aging proceeds, the system is capable of delivering accurate power prediction not only for room temperature, but also at lower temperatures at which power prediction is most challenging. Due to design property of ANN, the network parameters are adapted on-line to the current battery states (state-of-charge (SoC), state-of-health (SoH), temperature). SoC is required as an input parameter to SoAP module and high accuracy is crucial for a reliable on-line adaptation. Therefore, a reasonable way to determine the battery state variables is proposed applying a combination of several partly different algorithms. Among other SoC boundary estimation methods, robust extended Kalman filter (REKF) for recalibration of amp hour counters was implemented. ANFIS then achieves the SoAP estimation by means of time forward voltage prognosis (TFVP) before a power pulse occurs. The trade-off between computational cost of batch-learning and accuracy during on-line adaptation was optimized resulting in a real-time system with TFVP absolute error less than 1%. The verification was performed on a software-in-the-loop test bench setup using a 53 Ah lithium-ion cell.