We report the discovery of two ternary Zintl phases Ba3Sn3Sb4 and Ba(7x)Sn(11S)b(15y) (x = 0.4, y = 0.6). Ba3Sn3Sb4 adopts the monoclinic space group P2(1)/c with a = 14.669(3) angstrom, b = 6.9649(14) angstrom, c = 13.629(3) angstrom, and beta = 104.98(3)degrees. It features a unique corrugated two-dimensional (2D) structure consisting of [Sn3Sb4](6) layers extending along the ab-plane with Ba2+ atoms sandwiched between them. The nonstoichiometric Ba6.6Sn11Sb14.4 has a complex one-dimensional (1D) structure adopting the orthorhombic space group Pnma, with unit cell parameters a = 37.964(8) angstrom, b = 4.4090(9) angstrom, and c = 24.682(5) angstrom. It consists of large double SnSb ribbons separated by Ba2+ atoms. Ba3Sn3Sb4 is an n-type semiconductor which has a narrow energy gap of similar to 0.18 eV and a room temperature carrier concentration of similar to 4.2 X 10(18) cm(-3). Ba6.6Sn11Sb14.4 is determined to be a metal with electrons being the dominant carriers.