The recent work of Saito and Shigemoto for deriving the Weinberg-Salam model from leptonic system is extended to a more realistic model including quarks. The photonand the weak-vector bosons are considered composites of lepton-antilepton or quark-antiquark pair while the color-octet gluons are considered those of quark-antiquark pair. The Weinberg angle is determined to be sin2θW = 3/8 for fractionally charged quarks, which coincides with the prediction of Georgi and Glashow in their unified gauge model. The gluon coupling constant is also determined to be 8/3 times the fine structure constant.