We have collected 10025 foreground-background quasar pairs with projected distances d_p_<500kpc from the large quasar catalog of the Sloan Digital Sky Survey DR16Q. We investigate the properties of the MgII absorption lines with W_r_>0.15{AA} around foreground quasars, including both the line of sight (LOS; of foreground quasars) and transverse (TRA; perpendicular to the LOS) absorptions. Both the equivalent width (the correlation coefficient {rho}=-0.915 and the probability P<10^-4^ of no correlation) and incident rate ({rho}=-0.964 and P<10^-6^) of TRA MgII absorption lines are obviously anticorrelated with projected distance. The incident rate of TRA MgII absorption lines is obviously (>4{sigma}) greater than that of LOS MgII absorption lines at projected distances d_p_<200kpc, while the TRA and LOS MgII both have similar (<3{sigma}) incident rates at scales d_p_>200kpc. The anisotropic radiation from quasars would be the most possible interpretation for the anisotropic absorption around quasars. This could also indicate that the quasar radiation is not obviously impacting the gas halos of quasars at scales d_p_>200kpc.