UNiSi₂ orders ferromagnetically below T_Curie 95 K. This material crystallizes in the orthorhombic CeNiSi₂-type structure. The uranium atoms form double-layers, which are stacked along the crystallographic b axis (the longest axis). From magnetization measurements the easy (hard) magnetization axis is the c axis (b axis). ²⁹Si-NMR measurements have been performed in the paramagnetic state. In UNiSi₂, two crystallographic Si sites exist with orthorhombic local symmetry. The Knight shifts on each Si sites have been estimated from these spectra of random and oriented powders. The transferred hyperfine couplings have been also derived. It is found that the transferred hyperfine coupling constants on each Si sites are nearly isotropic, and that their Knight shift anisotropy comes from that of the bulk susceptibility. The nuclear-spin lattice relaxation rate 1/T₁ shows temperature-independent behaviour, which indicates the existence of localized 5f electrons.