We develop a new nonwoven composite separator for a safer lithium-ion battery, which is based on coating of silica ($SiO_2$) colloidal particles/styrene-butadiene rubber (SBR) binder to a poly(ethylene terephthalate) (PET) nonwoven support. The $SiO_2$ particles are interconnected by the SBR binder and closely packed in the nonwoven composite separator, which thus allows for the development of unusual porous structure, i.e. highly-connected interstitial voids formed between the $SiO_2$ particles. The PET nonwoven serves as a mechanical support that contributes to suppressing thermal shrinkage of the nonwoven composite separator. The $SiO_2$/SBR content in the nonwoven composite separators plays an important role in determining their separator properties. Porous structure, air permeability, and electrolyte wettability of the nonwoven composite separators, in comparison to a commercialized polyethylene (PE) separator, are elucidated as a function of the $SiO_2$/SBR content. Based on this understanding of the nonwoven composite separators, the effect of $SiO_2$/SBR content on the electrochemical performances such as self-discharge, discharge capacity, and discharge C-rate capability of cells assembled with the nonwoven composite separators is investigated.