This paper presents the development of a constitutive model for describing the nonlinear viscoelastic behavior of deep-seabed sediments. To quantify the nonlinear response, shear rheological tests are carried out on deep-sea sediments substitute at different shear rates. These substitute samples are prepared by mixing bentonite with water based on the in-situ vane shear strength of deep-sea sediments. A compressible viscoelastic fluid model is formulated based on the thermodynamic framework developed by Rajagopal and Srinivasa (2000) to describe the experimental response of bentonite–water mixture. Experimental responses indicate that the effects of slip are significant in the shear rheometry of bentonite–water mixture. Hence a slip model is proposed, which relates the shear stress to slip velocity at the wall and the imposed shear rate values. The slip boundary conditions coupled with the viscoelastic model is validated using experimental data and is observed to be in good agreement. Further, the influence of shear rate on interfacial slip has been numerically analyzed and slip effects are found to be significant in defining rheological behavior with increasing shear rates. © 2019 Elsevier Ltd