Lithium-ion batteries are used as the main power source in many electronic and electrical devices. In particular, with the growth in battery-powered electric vehicle development, the lithium-ion battery plays a critical role in the reliability of vehicle systems. In order to provide timely maintenance and replacement of battery systems, it is necessary to develop a reliable and accurate battery health diagnostic that takes a prognostic approach. Therefore, this paper focuses on two main methods to determine a battery's health: (1) Battery State-of-Health (SOH) monitoring and (2) Remaining Useful Life (RUL) prediction. Both of these are calculated by using a filter algorithm known as the Support Vector Regression-Particle Filter (SVR-PF). Models for battery SOH monitoring based on SVR-PF are developed with novel capacity degradation parameters introduced to determine battery health in real time. Moreover, the RUL prediction model is proposed, which is able to provide the RUL value and update the RUL probability distribution to the End-of-Life cycle. Results for both methods are presented, showing that the proposed SOH monitoring and RUL prediction methods have good performance and that the SVR-PF has better monitoring and prediction capability than the standard particle filter (PF).