We present a stellar population synthesis study of a type I luminous infrared galaxy (LIRG): IRAS F13308+5946. It is a quasar with absolute magnitude Mi = -22.56 and has a spectral feature of a Seyfert 1.5 galaxy. Optical images show characteristics of later stages of a merger. With the help of the stellar synthesis code STARLIGHT (Cid Fernandes et al. 2005) and both Calzetti et al. (2000) and Leitherer et al.'s (2002) extinction curves, we estimate the past infrared (IR) luminosities of the host galaxy and find it may have experienced an ultraluminous infrared galaxy (ULIRG) phase for nearly 300 Myr, so this galaxy has probably experienced a type I ULIRG phase. Both nuclear starburst and active galactic nuclei (AGN) contribute to the present IR luminosity budget, and starburst contributes ~70%. The mass of supermassive black-hole (SMBH) is M_BH = 1.8*10^8 M_sun and the Eddington ratio L_bol/L_Edd is 0.12, which both approximate to typical values of PG QSOs. These results indicate that IRAS F13308+5946 is probably at the transitional phase from a type I ULIRG to a classical QSO.