Accurate estimation of the State of Power (SoP) can ensure safe and efficient operation of Lithium-ion batteries in Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs). The cell-to-cell variation within a battery pack is a major challenge towards accurate estimation of the SoP, particularly when the cells get aged. This paper presents a hybrid model predictive and fuzzy logic based control system to accurately estimate the SoP for series-connected Lithium-ion cells. The estimation strategy consists of two steps; the power capability for a single new cell is first reckoned under the light of the model predictive control algorithm. The second step is devoted to designation of a model-less fuzzy logic based control system to compensate for the concurrent aging state and State of Charge (SoC) differences among the cells. Accordingly, the present approach only utilizes the actual values of current and cell voltages together with the Electric Circuit Model (ECM) parameters of the new cell, which are identified off-line. Moreover, it benefits from a closed-loop framework which ends in an accurate and reliable SoP estimation. An experimental setup consisting of fresh and aged LiFePO4 cell samples is designed and the extracted data are utilized to verify the proposed estimation method in a feed-forward simulation model for a HEV. The results indicate that the proposed method can estimate the pack SoP accurately while the safe operation for the cells is guaranteed.