In this paper, the dependence of the broad Fe Kα line on the physical parameters of AGN, such as the black hole mass M_BH, accretion rate (equivalently represented by Eddington ratio λ_Edd) and optical classification is investigated by applying the X-ray spectra stacking method to a large sample of AGN which have well measured optical parameters. A broad-line feature is detected (>3σ) in the stacked spectra of the high λ_Edd sub-sample (log λ_Edd > −0.9). The profile of the broad line can be well fitted with relativistic broad-line model, with the line energy consistent with highly ionized Fe Kα line (i.e. Fe xxvi). A model consisting of multiple narrow lines cannot be ruled out, however. We found hints that the Fe K line becomes broader as the λ_Edd increases. No broad-line feature is shown in the sub-sample of broad-line Seyfert 1 (BLS1) galaxies and in the full sample, while a broad line might be present, though at low significance, in the sub-sample of narrow-line Seyfert 1 (NLS1) galaxies. We find no strong dependence of the broad line on black hole masses. Our results indicate that the detection/properties of the broad Fe Kα line may strongly depend on λ_Edd, which can be explained if the ionization state and/or truncation radius of the accretion disc changes with λ_Edd. The non-detection of the broad line in the BLS1 sub-sample can be explained if the average equivalent width of the relativistic Fe Kα line is weak or/and the fraction of sources with relativistic Fe Kα line is small in BLS1 galaxies.