The creep behaviors of expansive soils play an important role in landslide prediction and long-term stability analysis. In this paper, triaxial drained compression creep tests of expansive soils were conducted on the improved stress-controlled triaxial apparatus. The test results show that only transient deformation and attenuation creep occur with low deviator stress, and the increment of axial strain increases exponentially with deviator stress increasing; while deviator stress reaches a certain value, attenuation creep, steady creep and accelerated creep all occur in a creep curve. Meanwhile, the volumetric strain presents the shear shrinkage characteristic at the initial stage of loading, and the shear shrinkage is small. With the extension of loading time, the volumetric strain gradually varies from shear contraction to dilatancy. When entering the accelerated creep stage, the development rate of volumetric strain increases sharply. Besides, isochronous stress-strain curves of expansive soils indicate that their creep process possesses nonlinear characteristics, and the nonlinear degree is related to creep time and stress level. Imitating the empirical formula of cyclic cumulative deformation of clay, a new nonlinear creep model is presented, which may well describe the creep property of expansive soils. Furthermore, critical failure stress could be obtained based on the proposed creep model. The ratio of the critical failure stress to conventional shear failure stress ranges from 70% to 80%, with average of 75.56%, therefore, critical failure stress may be estimated by conventional triaxial tests with the margin of error 5.5% within.