We report detections of 39 2175{AA} dust extinction bump candidates associated with strong MgII absorption lines at z~1-1.8 on quasar spectra in Sloan Digital Sky Survey (SDSS) DR3. These strong MgII absorption line systems are detected among 2951 strong MgII absorbers with a rest equivalent width W_r_{lambda}2796>1.0{AA} at 1.0<z<1.86, which is part of a full sample of 7421 strong MgII absorbers compiled by Prochter et al. (2006, Cat. J/ApJ/639/766). The redshift range of the absorbers is chosen to allow the 2175{AA} extinction features to be completely covered within the SDSS spectrograph operation wavelength range. An upper limit of the background quasar emission redshift at z=2.1 is set to prevent the Ly{alpha} forest lines from contaminating the sensitive spectral region for the 2175{AA} bump measurements. A total of 12 absorbers are detected with 2175{AA} bumps at a 5{sigma} level of statistical significance, 10 are detected at a 4{sigma} level, and 17 are detected at a 3{sigma} level. Most of the candidate bumps in this work are similar to the relatively weak 2175{AA} bumps observed in the Large Magellanic Cloud LMC2 supershell rather than the strong ones observed in the Milky Way.