An object is to provide a battery-separator nonwoven fabric and a battery separator that are excellent in heat resistance, have a small pore diameter, and have a high tensile elongation and a high thrust strength, and a solution is to configure a battery-separator nonwoven fabric with a fiber A including a nanofiber having a fiber diameter of 100 to 1000 nm, a fiber B including a thermal adhesive ultrafine fiber having a fiber diameter of 100 to 2000 nm, and a fiber C including a thermal adhesive fiber having a single fiber fineness of 0.1 dtex or more, in which a tensile elongation of the nonwoven fabric is 10% or more.