Compared to high ionization CIV absorption lines, variable MgII absorption lines are rare. Using spectra from the Sloan Digital Sky Survey, we investigate the variations in MgII narrow absorption lines (NALs) for quasars with multi-epoch observations. We have compiled 8958 MgII NALs in the spectral regions from the red wings of CIV emission lines to the red wings of MgII emission lines. Among these 8958 MgII NALs, 22 variable NALs are detected with |{Delta}W_r_^{lambda}2796^|>=3{sigma}_W_ and with velocity offsets ranging from {upsilon}_r_=522 to 145513km/s. We find that: (1) the detected frequency of MgII NALs with {upsilon}_r_<=10000km/s is significantly larger than the uniformly random value expected for the MgII NALs with {upsilon}_r_>10000km/s, (2) the incidence rates of the variable MgII NALs with {upsilon}_r_<=10000km/s are much larger than those with {upsilon}_r_>10000km/s, (3) the velocity offsets of variable MgII NALs with {upsilon}_r_<=10000km/s are much smaller than the maximum velocities expected from radiation-driven outflows, and (4) the variations of variable MgII NALs with {upsilon}_r_<=10000km/s are obviously correlated with the changes in the quasar radiative output. Therefore, the 16 variable MgII NALs, whose velocities are smaller than the maximum velocities expected from radiation-driven outflows, are likely related to quasar outflows, while the 6 variable MgII NALs, whose velocities are much larger than the maximum velocities expected from radiation-driven outflows, possibly originated in intervening gas. We also find that both the variations and fractional variations in absorption strengths are not related to the velocity offsets of MgII NALs and the time intervals between the two epochs of observations. Also, the fractional variations in absorption strengths are inversely correlated with absorption strengths. In addition, both the associated and intervening MgII NALs can significantly vary on a timescale of days.