The properties of host galaxies associated with fast radio bursts (FRBs) provide critical information for inferring the progenitors and radiation mechanisms of these bursts. We report on the host galaxy of the repeating FRB 20190520B, a dwarf galaxy at the spectroscopic redshift z = 0.241 with a stellar mass of (6.2 +/- 0.8) x 108 M circle dot. The emission-line ratios suggest that the ionized gas is powered by star formation. The total H alpha-traced star formation rate (SFR) is 0.70 +/- 0.01 M circle dot yr-1, and the metallicity is 12+log10([O/H])>= 7.4 +/- 0.1 . The specific star formation rate (sSFR) is logsSFR/yr-1=-9.0 +/- 0.1 , higher than the upper limit of -9.4 observed in nearby dwarf galaxies. The dispersion measure (DM) contribution from the host galaxy is estimated to be DMhost approximate to 950 +/- 220 pc cm-3, based on the H alpha emission. The FRB and the associated persistent radio source are located at the H alpha emission peak, offset by similar to 1 .' 4 (5.5 kpc) in projection from the stellar continuum. At this position, the lower limit of logsSFR/yr-1 is -8.5 +/- 0.1, more than 3 times the galaxy's total sSFR. The H alpha velocity difference between the stellar continuum and the offset gas is 39.6 +/- 0.4 km s-1, which is sufficient to draw conclusions about the nature of the offset.