Non-aqueous electrolyte secondary battery cell having safety and increased energy density, and battery using same. The cell is shaped as a rounded square tube. A core material for preventing electrolyte permeation is at the cell center, the core member being a hollow cylindrical insulator of square cross-section. A cell monitoring system such as a temperature sensor is provided in the hollow part of the core material. A cell base member including positive electrode member, separator, and negative electrode member of a non-aqueous electrolyte secondary battery is wound around the core material. Terminals made of electroconductive metal electrically connected to the collector of the positive electrode member or the collector of the negative electrode member are exposed to the cell exterior. The temperature sensor is attached to the center part of the hollow part of the core material in close contact with the core material.