The Galactic black hole candidate MAXI J0637-430 was first discovered by MAXI/GSC on 2019 November 2. We study the spectral properties of MAXI J0637-430 by using the archived NuSTAR data and Swift/XRT data. After fitting the eight spectra by using a disk component and a powerlaw component model with absorption, we select the spectra with relatively strong reflection components for detailed X-ray reflection spectroscopy. Using the most state-of-art reflection model, relxillCp, the spectral fitting measures a black hole spin a* > 0.72 and the inclination angle of the accretion disk i = \(46.1^{+4.0}_{-5.3}\) degrees, at a 90% confidence level. In addition, the fitting results show an extreme supersolar iron abundance. Combined with the fitting results of reflection model reflionx_hd, we consider that this unphysical iron abundance may be caused by a very high-density accretion disk (ne > 2.34 × 1021 cm−3) or a strong Fe Kα emission line. The soft excess is found in the soft state spectral fitting results, which may be an extra free–free heating effect caused by high density of the accretion disk. Finally, we discuss the robustness of black hole spin obtained by X-ray reflection spectroscopy. The result of relatively high spin is self-consistent with broadened Fe Kα line. Iron abundance and disk density have no effect on the spin results.