ABSTRACT We report the results of the rapid follow-up observations of gamma-ray bursts (GRBs) detected by the Fermi satellite to search for associated fast radio bursts. The observations were conducted with the Australian Square Kilometre Array Pathfinder at frequencies from 1.2 to 1.4 GHz. A set of 20 bursts, of which four were short GRBs, were followed up with a typical latency of about 1 min, for a duration of up to 11 h after the burst. The data were searched using 4096 dispersion measure trials up to a maximum dispersion measure of 3763 pc cm−3, and for pulse widths w over a range of duration from 1.256 to 40.48 ms. No associated pulsed radio emission was observed above $26 \, {\rm Jy\, ms}\, (w/1\, {\rm ms})^{-1/2}$ for any of the 20 GRBs.