The rapid neutron-capture process (r-process) is a major process to synthesize elements heavier than iron, but the astrophysical site(s) of r-process is not identified yet. Neutron star mergers (NSMs) are suggested to be a major r-process site from nucleosynthesis studies. Previous chemical evolution studies however require unlikely short merger time of NSMs to reproduce the observed large star-to-star scatters in the abundance ratios of r-process elements relative to iron, [Eu/Fe], of extremely metal-poor stars in the Milky Way (MW) halo. This problem can be solved by considering chemical evolution in dwarf spheroidal galaxies (dSphs) which would be building blocks of the MW and have lower star formation efficiencies than the MW halo. We demonstrate that enrichment of r-process elements in dSphs by NSMs using an N-body/smoothed particle hydrodynamics code. Our high-resolution model reproduces the observed [Eu/Fe] by NSMs with a merger time of 100 Myr when the effect of metal mixing is taken into account. This is because metallicity is not correlated with time up to ~ 300 Myr from the start of the simulation due to low star formation efficiency in dSphs. We also confirm that this model is consistent with observed properties of dSphs such as radial profiles and metallicity distribution. The merger time and the Galactic rate of NSMs are suggested to be <~ 300 Myr and ~ $10^{-4}$ yr$^{-1}$, which are consistent with the values suggested by population synthesis and nucleosynthesis studies. This study supports that NSMs are the major astrophysical site of r-process.
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