We present chemical abundance determinations of two H II regions in the dwarf irregular (dIrr) galaxy Leo A from Gran Telescopio Canarias (GTC) Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) long-slit spectra. Both H II regions are of low excitation and seem to be ionized by stars later than O8V spectral type. In one of the H II regions we used the direct method: O+2 ionic abundance was calculated using an electronic temperature determined from the [O III] λλ4363/5007 line ratio; ionic abundances of O+, N+, and S+ were calculated using a temperature derived from a parametrized formula. O, N, and S total abundances were calculated using ionization correction factors from the literature for each element. Chemical abundances using strong-line methods were also determined, with similar results. For the second H II region, no electron temperature was determined thus the direct method cannot be used. We computed photoionization structure models for both H II regions in order to determine their chemical composition from the best-fitting models. It is confirmed that Leo A in a very low metallicity galaxy, with 12 + log(O/H) = 7.4 ± 0.2, log(N/O) = -1.6, and log(S/O) = -1.1. Emission lines of the only planetary nebula (PN) detected in Leo A were re-analysed and a photoionization model was computed. This PN shows 12 + log(O/H) very similar to the ones of the H II regions and a low N abundance, although its log(N/O) ratio is much larger than the values of the H II regions. Its central star seems to have had an initial mass lower than 2 M⊙.