By assuming that only gravitation acts between dark matter (DM) and normalmatter (NM), we study the effects of fermionic DM on the properties of neutron stars using the two-fluid Tolman-Oppenheimer-Volkoff formalism. It is found that the mass-radius relationship of the DM admixed neutron stars (DANSs) depends sensitively on the mass of DM candidates, the amount of DM, and interactions among DM candidates. The existence of DM in DANSs results in a spread of mass-radius relationships that cannot be interpreted with a unique equilibrium sequence. In some cases, the DM distribution can surpass the NM distribution to form a DM halo. In particular, it is favorable to form an explicit DM halo, provided the repulsion of DM exists. It is interesting to find that the difference in particle number density distributions in DANSs and consequently in star radii caused by various density dependencies of nuclear symmetry energy tends to disappear as long as the repulsion of accumulated DM is sufficient. These phenomena indicate that the admixture of DM in neutron stars can significantly affect the astrophysical extraction of nuclear EOS by virtue of neutron star measurements. In addition, the effect of the DM admixture on the star maximum mass is also investigated.