Structural and electronic properties of ternary compounds Bi2-xSbxTe3 and quaternary compounds Bi2-xSbxTe3-ySey are investigated by using the density functional theory within full potential-linearized augmented plane wave method. The structural properties of compounds are examined using the Murnaghan equation of state, which also contains experimental data for comparison. Specifically, band structures exhibit very similar behaviour in total density of states of compounds which show narrow-gap semiconductor material characteristics. Bi1.66Sb0.33Te3, Bi1.33Sb0.66Te3, BiSbTe3, Bi0.66Sb1.33Te3 and Bi0.33Sb1.66Te3 are direct band gap materials and the band gap energies of these compounds are found to depend linearly on compound composition x. Bi1.66Sb0.33Te2.66Se0.33, Bi1.33Sb0.66Te2.33Se0.66, BiSbTe2Se, Bi0.66Sb1.33Te1.66Se1.33, Sb2TeSe2, Sb2Te0.66Se2.33 and Sb2Te0.33Se2.66 are direct band gap materials and the band gap energies of these compounds are found to depend non-linearly on compound composition x and y. This theoretical work will be of great interest in ternary and quaternary semiconductor research.