This paper proposes a new self-cognizant dynamic system approach for Battery PHM, that incorporates an artificial neural network model into a dual extended Kalman filter (DEKF) algorithm. A feed-forward neural network (FFNN) structure is employed to approximate a complex battery system response that is mostly treated as impossible modeling work due to inaccessible system physics. After training by historical data, the FFNN model is embedded into a DEKF algorithm to track down system dynamics. The required recursive computation, which is used to update the FFNN model during collecting the online measurement, is also derived in this paper. To validate the proposed SCDS approach, a battery dynamic system is introduced as an experimental application. After modeling the battery system by an FFNN model and a state-space model, the state-of-charge (SoC) and state-of-health (SoH) are estimated with updating the FFNN model by the proposed approach. Experimental results illustrate that the proposed approach improves the efficiency and accuracy for battery PHM.