This paper develops and analyzes a mathematical model for the novel system of a redox flow lithium ion battery (RFLB). In essence, the model accounts for conservation of charge in the cell and conservation of species - redox shuttle molecules - in both the cell and tanks. In order to gain further understanding of the system involving multiple redox species, the steady-state conservation of charge in the cell is analyzed. Such an analysis allows for a considerable reduction in model complexity, resulting in a semi-analytical model. The results of the semi-analytical model are verified against those of full model and validated with experimental charge-discharge curves. Overall, good agreement is found that allows the model to explain the system behavior, particularly the multiple voltage regimes and the corresponding electrochemical and chemical reactions taking place. An operational strategy for improving the battery capacity is identified. (C) 2017 Published by Elsevier Ltd.