A single crystal of bismuth diselenide, BiSe2, containing both monochalcogen (Se2-) and dichalcogen (Se-2(2-)) ions, was prepared at a high pressure of 5.5 GPa. Its crystal structure, substitution chemistry, and physical properties were investigated. X-ray analysis showed that BiSe2 is in a monoclinic system (space group C2/m) with the following lattice parameters: a = 16.740(3) angstrom, = 4.1410(11) angstrom, c = 12.027(3) angstrom, and beta = 127.658(13)degrees. A crystal structure of BiSe2 can be viewed as a layered structure with stacks of neutral BiSe2 blocks along the c-axis, or alternatively as a quasi-one-dimensional structure with double chains of BiSe5 pyramids along the b-axis. Each Bi is coordinated with three Se2- ions and two Se-2(2-) ions, and the bond valence analysis indicated that Bi was trivalent. BiSe2 and BiS2 form a solid solution in the whole range while retaining the same structure, and the partial substitution of Sb for Bi is also achieved at 10%. All the compounds show a semiconducting property and diamagnetism that can be attributed to the closed-shell ion core. In spite of the compositional analogy with Bi2Se3, BiSe2 is proven by the first-principles calculations not to be a topological insulator.