A battery separator of the invention is obtained by press forming a meltblown nonwoven fabric comprising 4-methyl-1-pentene polymer or a 4-methyl-1-pentene/.alpha.-olefin copolymer, the battery separator having an average fiber diameter of 0.8 to 5 .mu.m, a basis weight of 9 to 30 g/m.sup.2, a porosity of 30 to 60%, and a load at 5% elongation in the MD direction (longitudinal direction) of not less than 1.2 (kg/5 cm width). A lithium ion secondary battery of the invention includes the battery separator.