The goal of our serial papers is to examine the evolutionary connection between AGN and star formation in its host galaxy in the partially obscured AGNs (i.e., Seyfert 1.8 and 1.9 galaxies). Taking advantage of these galaxies, the properties of both components can be studied together by direct measurements. In this paper, we focus on the broad-line composite galaxies (composite AGNs) which are located between the theoretical and empirical separation lines in the [NII]/Ha vs. [OIII]/Hb diagram. These galaxies are searched for from the composite galaxies provided by the SDSS DR4 MPA/JHU catalogs. After re-analyze the spectra, we perform a fine classification for the 85 composite AGNs in terms of the BPT diagrams. All the objects located below the three theoretical separation lines are associated with a young stellar population (<1Gyrs), while either a young or old stellar population is identified in the individual multiply-classified object. The multiply-classified objects with a very old stellar population are located in the LINER region in the [OI]/Ha vs. [OIII]/Hb diagram. We then consider the connection between AGN and star formation to derive the key results. The Eddington ratio inferred from the broad Ha emission, the age of the stellar population of AGN's host as assessed by D_n(4000), and the line ratio [OI]/Ha are found to be related with each other. These relations strongly support the evolutionary scenario in which AGNs evolve from high L/L_Edd state with soft spectrum to low L/L_Edd state with hard spectrum as young stellar population ages and fades. The significant correlation between the line ratio [OI]/Ha and D_n(4000) leads us to suggest that the line ratio could be used to trace the age of stellar population in type I AGNs.