The polyolefin spunbonded nonwoven fabric is defined as (A) being formed of continuous polyolefin fibers having a fineness of 0.5 to 3 denier, (B) having basic weight between 30 g/m.sup.2 and 15 g/m.sup.2, and (C) having .sqroot.S.sub.MD .times.S.sub.TD of 2.5 g or below, wherein S.sub.MD and S.sub.TD are respectively the softnesses in the machine and transverse directions as measured by a handle-O-meter. The method of producing a strip of very soft polyolefin nonwoven fabric by directing polyolefin continuous fibers in a fixed direction, comprises the steps of: orienting the axes of the continuous fibers in the direction in which the continuous fibers are fed so as to form a web having a warp orientation factor (the maximum tensile strength in the direction in which the continuous fibers are fed, i.e., in a machine direction/the maximum tensile strength in a transverse direction) of 3.0 or above; and then applying wave-like crepes propagated in the machine direction to the web by creping the web.