Prognostic and condition-based maintenance of lithium-ion batteries is a fundamental topic, which is rapidly expanding since a long battery lifetime is required to ensure economic viability and minimize the life cycle cost. Remaining useful life (RUL) estimation is an essential tool for prognostic and health management of batteries. In this article, a hybrid approach based on both condition monitoring and physic model is presented to improve the accuracy and precision of RUL estimation for lithium-ion battery. An artificial intelligence estimation method based on recurrent neural network (RNN) is integrated with a state-space estimation technique, which is typical of filtering-based approach. The state-space estimation is used to generate a big dataset for the training of the RNN. Some additional deep layers are used to improve the prediction of nonlinear trends (typical of batteries), while the performance optimization of the RNN is ensured using a genetic algorithm. The performances of the proposed method have been tested using a battery degradation dataset from the data repository of Prognostics Center of Excellence at NASA. Two different degradation models are compared, the widely known empirical double exponential model and an innovative single exponential model that allows to ensure optimal performance with fewer parameters required to be estimated.