Nuclear mass, β-decay half-life, and neutron-capture rate are the most important nuclear physics inputs for rapid-neutron capture process (r-process) simulations. Nuclear mass can directly impact the abundance ratio of neighboring isotopes during the (n,γ)-(γ,n) equilibrium stage. On the other hand, nuclear mass influences the predictions of β-decay half-lives and the neutron-capture rates, thus indirectly impacting the r-process simulation. Currently, only about 3000 nuclear masses have been precisely measured in experiments, and many of the nuclear masses involved in r-process simulations can only be predicted by theory models. However, when extrapolating nuclear masses towards the neutron drip line, there are large discrepancies between the predictions of different mass models, which inevitably affects the predictions of β-decay half-lives and neutron-capture rates. In this work, ten mass models are employed to systematically study the impact of nuclear mass uncertainties on β-decay half-lives and neutron-capture rates. The β-decay half-lives and neutron-capture rates are calculated by the β-decay half-life semi-empirical formula and TALYS code, respectively. It has been found that the uncertainties in nuclear mass predictions among different mass models can reach 10 MeV in the neutron-rich region; the differences between the maximum and minimum masses predicted by these models even exceed 30 MeV for some nuclei. For the predictions of β-decay energy Qβ and (n, γ) reaction energy Q(n,γ), there are large deviations mainly around the neutron magic numbers and close to the neutron drip line, with uncertainties about 1 MeV and 2 MeV, respectively. The impact of mass uncertainties on the β-decay half-lives is about 0.6 orders of magnitude for neutron-rich nuclei. The uncertainties of neutron-capture rates increase significantly when extrapolating towards the neutron-rich region. At the temperature of T = 10⁹ K, the average uncertainties of neutron-capture rates range over 2 ∼ 3 orders of magnitude for nuclei near neutron drip line. Taking N = 50, 82, 126, 184 isotones as examples, it is found that the differences between the maximum and minimum neutron-capture rates obtained from various nuclear mass models even exceed 10 orders of magnitude for some nuclei. The Q_(n,γ) directly impacts the trend of the neutron-capture rates, and the neutron-capture rates are very sensitive to the uncertainties of Q_(n,γ) for neutron-rich nuclei. In addition, the effect of temperature on neutron-capture rates has also been investigated, and it is found that the increase in temperature can reduce the impact of mass uncertainties on the predictions of neutron-capture rates for neutron-rich nuclei. In this work, the β-decay half-lives and neutron-capture rates are calculated based on ten mass tables. Therefore, more self-consistent nuclear physics inputs will be provided for the simulation of the r-process. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00222 (Please use the private access link https://www.scidb.cn/s/iyIZFf to access the dataset during the peer review process).