To obtain a finely porous polyolefin fiber having good adsorbing properties, excellent in thermal stability, chemical resistance and strength and useful for a superprecise air filter by forming a specific polyolefin composition into a filamentous shape and drawing the same.

This finely porous polyolefin fiber is obtained by mixing an alkoxysilane with water or mixing a vinyl monomer (e.g. styrene), a cross- linking agent and a radical polymerization initiator in a melt of a polyolefin such as polyethylene and polypropylene to synthesize fine polysiloxane particles or fine vinyl polymer particles having 0.01-0.1μm average particle diameter, forming the polyolefin composition including obtained particles dispersed therein without substantially forming coagulated particles into filamentous shape, drawing it to provide the objective porous polyolefin fiber including continuos pores having 0.005-0.1μm average pore diameter, 1-25% porosity and 40-200m2/g whole pore specific surface area.