We present detailed timing and spectral studies of the black hole candidate MAXI J0637–430 during its 2019–2020 outburst using observations with the Neutron Star Interior Composition Explorer (NICER)and the Neil Gehrels Swift Observatory. We find that the source evolves through the soft-intermediate, high-soft, hard-intermediate, and low-hard states during the outburst. No evidence of quasi-periodic oscillations is found in the power-density spectra of the source. Weak variability with fraction alarms amplitude<5 per cent is found in the softer spectral states. In the hard-intermediate and hard states, high variability with the fractional rms amplitude of>20 per cent is observed. The 0.7–10 keV spectra with NICER are studied with a combined disc-black-body and nth comp model along with the interstellar absorption. The temperature of the disc is estimated to be 0.6 keV in the rising phase and decreased slowly to 0.1 keV in the declining phase. The disc component was not detectable or absent during the low-hard state. From the state-transition luminosity and the inner edge of the accretion flow, we estimate the mass of the black hole to be in the range of 5–12 M , assuming the source distance of d<10 kpc.