ABSTRACT We present a pilot study of extragalactic H i 21-cm absorption lines using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We observed five continuum sources with H i absorption features first identified in the 40 per cent data release of the Arecibo Legacy Fast Arecibo L-Band Feed Array (ALFA) Survey (ALFALFA), including two systems later detected by the Westerbork Synthesis Radio Telescope (WSRT). Most of our observations were carried out during the FAST commissioning phase, and we have tested different observing modes, as well as data reduction methods, to produce the best spectra. Our observations successfully confirmed the existence of H i absorption lines in all these systems, including two sources that were marginally detected by ALFALFA. We fitted the H i profiles with single or double of Gaussian functions, and calculated the H i column densities of each source. The H i absorption profiles obtained by FAST show much higher spectral resolution and higher SNR ratio than the existing data in the literature, thus demonstrating the power of FAST in revealing detailed structures of H i absorption lines. Our pilot observations and tests have enabled us to develop a strategy to search for H i absorption sources using the data from the FAST extragalactic H i survey, which is one of the key projects undertaken at FAST. We expect that over 1500 extragalactic H i absorbing systems could be detected with survey data, based on sensitivity level that we achieved in pilot observations.