  We report detections of 39 2175-{\AA} dust extinction bump candidates
associated with strong Mg II absorption lines at z$\sim$ 1--1.8 on quasar
spectra in Sloan Digital Sky Survey (SDSS) DR3. These strong Mg II absorption
line systems are detected among 2,951 strong Mg II absorbers with the rest
equivalent width $W_r\lambda2796 >$ 1.0{\AA} at $1.0 < z < 1.86$, which is part
of a full sample of 7,421 strong Mg II absorbers compiled by Prochter et al.
(2006). 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. The FM90 (Fitzpatrick & Massa 1990) parameterization is applied
to model the Optical/UV extinction curve in the rest frame of Mg II absorbers
of the 2175-{\AA} bump candidates. The simulation technique developed by Jiang
et al. (2010a, b) is used to derive the statistical significance of the
candidate 2175-{\AA} bumps. 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 Clouds (LMC) LMC2 supershell rather than
the strong ones observed in the Milky Way (MW). This sample has greatly
increased the total number of 2175-{\AA} extinction bumps measured on SDSS
quasar spectra. Follow-up observations may rule out some of possible false
detections and reveal the physical and chemical natures of 2175-{\AA} quasar
absorbers.
