A new approach to the quark potential model, the Composite Particle Representation Theory (CPRT), is introduced. The result of baryon spectra is presented to show the validity of applying this method to the quark physics. In this calculation, a baryon is able to be treated as one boson (diaquark) plus one quark system with quark-diquark effective interaction obtained from the original quark-quark interaction. The predicted baryon masses for the ground and first excited states are in good agreement with observations, and with no further adjustment of the 8 parameters in the qucark-quark effective interaction, which are determined by fitting the meson spectrum. These results suggest that the CPRT approach may be a powerful one for dealing with hadronic structure and scatterincg problems. Possible applications of this method in quark physics are discussed.