In this paper, the equilibrium geometries, one-, two-, and three-photon absorption properties, and the transition nature of a series of Y-shaped molecules which possess an imidazole-thiazole core have been theoretically studied by using the parametrization model 3 and Zerner's intermediate neglect of differential overlap methods. Our calculated results have confirmed the experimental findings that the investigated molecules are all promising multiphoton absorption materials and both the two-photon absorption and the three-photon absorption cross sections are seriatim increscent along with the increase of the electron-donor strength. The nonlinear optical phenomenon originates from the intramolecular charge transfer within the pi-conjugated system. The calculated results indicate that the heterocyclic core increases the two- and three-photon absorption cross sections due to its pi-excessive nature. So it can provide more free electrons to enlarge the charge transfer within the molecule system. In addition, the design of Y shape and the sulfonyl-based electron-accepting group play a part in the enhancement of multiphoton absorption. It is notable that molecules with heterocyclic core will provide favorable condition for multiphoton absorption applications.