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Iron line spectroscopy has been one of the leading methods not only for measuring the spins of accreting black holes but also for testing fundamental physics. Basing on such a method, we present an analysis of a data set observed simultaneously by NuSTAR and NICER for the black hole binary candidate MAXI J1803-298, which shows prominent relativistic reflection features. Various relxill _ nk flavors are utilized to test the Kerr black hole hypothesis. The results obtained from our analysis provide stringent constraints on Johannsen deformation parameter α _13 with the highest precise to date, namely ${\alpha }_{13}={0.023}_{-0.038}^{+0.071}$ from relxillD _ nk and ${\alpha }_{13}={0.006}_{-0.022}^{+0.045}$ from relxillion _ nk, respectively, in 3 σ credible lever, where the Johannsen metric reduces to the Kerr metric when α _13 vanishes. Furthermore, we investigate the best model fit results using Akaike information criterion and assess its systematic uncertainties.