A new generalization of the Oldroyd-B model is developed to describe the flow of blood. The model is developed within a thermodynamic framework which recognizes that a viscoelastic fluid can remain stress free in multiple configurations. The new model is an improvement over an earlier model developed within the same framework to describe the response characteristics of blood. It captures the shear-thinning and deformation-dependent viscoelastic behavior of blood just like the previous model. More importantly, unlike the previous model, it does not have the shortcoming of an abrupt transition of the material properties at low shear rates: instead, it allows for a smooth variation of the rate of dissipation, and therefore viscosity, over the entire range of physically feasible shear-rates. This feature is very attractive for developing high-fidelity numerical methods for application to the complex geometries that are typically encountered in the human vasculature. Convergence of the numerical method in simple geometries shows its superior properties as compared to the earlier model: this demonstration of model performance is a precursor to its use in 3D geometries. © 2013 Elsevier Ltd. All rights reserved.