In order to investigate the growth of supermassive black holes (SMBHs), we construct the black hole mass function (BHMF) and Eddington ratio distribution function (ERDF) of X-ray-selected broad-line active galactic nuclei (AGNs) at z~1.4 in the Subaru XMM-Newton Deep Survey (SXDS) field. A significant part of the accretion growth of SMBHs is thought to take place in this redshift range. Black hole masses of X-ray-selected broad-line AGNs are estimated using the width of the broad MgII line and 3000{AA} monochromatic luminosity. We supplement the MgII FWHM values with the H{alpha} FWHM obtained from our NIR spectroscopic survey. Using the black hole masses of broad-line AGNs at redshifts between 1.18 and 1.68, the binned broad-line AGN BHMFs and ERDFs are calculated using the V_max_ method. To properly account for selection effects that impact the binned estimates, we derive the corrected broad-line AGN BHMFs and ERDFs by applying the maximum likelihood method, assuming that the ERDF is constant regardless of the black hole mass. We do not correct for the non-negligible uncertainties in virial BH mass estimates. If we compare the corrected broad-line AGN BHMF with that in the local universe, then the corrected BHMF at z=1.4 has a higher number density above 10^8^M_{sun}_ but a lower number density below that mass range. The evolution may be indicative of a downsizing trend of accretion activity among the SMBH population. The evolution of broad-line AGN ERDFs from z=1.4 to 0 indicates that the fraction of broad-line AGNs with accretion rates close to the Eddington limit is higher at higher redshifts.