Ultraviolet (UV) nonlinear optical (NLO) crystals play an irreplaceable role as the key materials to realize the frequency conversion for all solid state lasers. To date, it is still difficult to design UV NLO crystals with large second harmonic generation (SHG) coefficients, moderate birefringences and wide band gaps. Benefiting from the large band gap, sulfate has become an important research direction of UV NLO crystals. However, since SO₄ is isotropic tetrahedral building units with nearly nonpolar T_d symmetry, it exhibits small microscopic second order polarizability and polarizability anisotropy, which tends to result in a weak SHG effect and small birefringence. In this work, we introduced Hg²⁺ ions that are easy to form distorted polyhedrons into the sulfates, resulting in a new NLO material, Rb₃Hg₂(SO₄)₃Cl. It crystallizes in a monoclinic space group (P2₁) with the lattice parameters a=0.78653(2) nm, b=0.97901(2) nm, c=1.00104(3) nm, and β=110.95(3) (Z=2). Structure of Rb₃Hg₂(SO₄)₃Cl consists of [SO₄] tetrahedra, [HgO₅] and [HgO₄Cl] polyhedral, which connected by a common corner to form a spatial 3D network. All the Rb atoms reside in the cavity of 3D network. The powder SHG measurement proposed by Kurtz and Perry indicates that Rb₃Hg₂(SO₄)₃Cl is a phase-matchable material in the visible region and exhibits a moderate SHG response about 1.5 times that of KH₂PO₄ (KDP). In addition, the UV-Vis-NIR diffuse reflectance spectral measurement indicates that Rb₃Hg₂(SO₄)₃Cl has a short UV cut-off edge of 251 nm, corresponding to the band gap of 4.94 eV. Its polarizing microscope measurement reveals that Rb₃Hg₂(SO₄)₃Cl has a moderate birefringence (The birefringence of Rb₃Hg₂(SO₄)₃Cl crystal at 546.1 nm is 0.04). Moreover, first-principles calculations uncover that the distorted [HgO₅], [HgO₄Cl] and [SO₄] polyhedral are responsible for its SHG effect. Our study shows that Rb₃Hg₂(SO₄)₃Cl may have potential applications as a UV NLO crystal.