By investigating properties from the infrared (IR) to the optical of IR-selected QSOs (IR QSOs), optically selected QSOs (PG QSOs), and narrow-line Seyfert 1 galaxies (NLS1s) in the local Universe, we find that the IR excess in IR QSOs is mostly in the far-IR, and their IR spectral indices suggest that the excess emission is caused by starbursts rather than AGNs. The ratio of the star formation rate and the accretion rate is about several hundred for IR QSOs, but decreases with the central black hole mass. We also study an optically selected QSO sample at high redshift with hyper-luminous far-IR luminosities. We find that similar to IR QSOs at low redshift, these high redshift QSOs have a far-IR excess also, which should be due to the contribution of starbursts heating the dust. But the ratio of star formation rate to accretion rate for QSOs at high redshift is typically smaller than that for IR QSOs at low redshift, which hints at the relatively faster growth of black holes at early epochs.