In this work, we propose and examine a battery system with a new design concept. The battery consists of a non-noble polyvalent metal (such as Ca, Mg, Al) combined with a positive electrode already well-established for lithium ion batteries (LIBs). The prototype demonstrated here is composed of a Mg negative electrode, LiFePO4 positive electrode, and tetrahydrofuran solution of two kinds of salts (LiBF4 and phenylmagnesium chloride) as an electrolyte. The LIB positive-electrode materials such as LiFePO4 can preferentially accommodate Li+ ions; i.e., they work as a "Li pass filter". This characteristic enables us to construct a septum-free, Daniel-battery type dual-salt polyvalent-metal storage battery (PSB). The presented dual-salt PSB combines many advantages, e.g., fast diffusion of Li+ ions in the positive electrode, high cyclability, and a high specific capacity of lightweight polyvalent metals. The concept is expected to allow the design of many combinations of dual-salt PSBs having a high energy density and high rate capability.