(57) The nonwoven fabric is made up of filaments comprised of a biodegradable polymer composed principally of a thermoplastic aliphatic polyester, wherein the filaments have a crystallization degree of 7 to 40 % and a supercool index of 0,4 or more. A method of fabricating the nonwoven fabric comprises the steps of melting the biodegradable polymer, said biodegradable polymer having a melt flow rate of 10 to 100 g/10 minutes as measured at 190°C according to ASTM-D-1238 (E), in a temperature range of from (Tm + 20)°C to (Tm + 80)°C, where Tm°C is the melting point of the biodegradable polymer; extruding the melt through a spinneret into filaments; drafting the extruded filaments by means of a suction device disposed below the spinneret under a quenching air blow of not more than 20°C generated through a conventional device and at a drafting speed of from 1,000 to 5,000 m/minute, thereby fining them down into finer filaments; then depositing such filaments, as they are spread open each other, and are laid up on a travelling collector surface to form a web; and heat-treating the web thereby to obtain the nonwoven fabric.