Directed cell migration plays a crucial role in physiological and pathological conditions. One important mechanical cue, known to influence cell migration, is the gradient of substrate elastic modulus (E). However, the cellular microenvironment is viscoelastic and hence the elastic property alone is not sufficient to define its material characteristics. To bridge this gap, in this study, we investigated the influence of the gradient of viscous property of the substrate, as defined by loss modulus (G) on cell migration. We cultured human mesenchymal stem cells (hMSCs) on a collagen-coated polyacrylamide gel with constant storage modulus (G) but with a gradient in the loss modulus (G). We found hMSCs to migrate from high to low loss modulus. We have termed this form of directional cellular migration as "Viscotaxis". We hypothesize that the high loss modulus regime deforms more due to creep in the long timescale when subjected to cellular traction. Such differential deformation drives the observed Viscotaxis. To verify our hypothesis, we disrupted the actomyosin contractility with myosin inhibitor blebbistatin and ROCK inhibitor Y27632, and found the directional migration to disappear. Further, such time-dependent creep of the high loss material should lead to lower traction, shorter lifetime of the focal adhesions, and dynamic cell morphology, which was indeed found to be the case. Together, findings in this paper highlight the importance of considering the viscous modulus while preparing stiffness-based substrates for the field of tissue engineering. STATEMENT OF SIGNIFICANCE: While the effect of substrate elastic modulus has been investigated extensively in the context of cell biology, the role of substrate viscoelasticity is poorly understood. This omission is surprising as our body is not elastic, but viscoelastic. Hence, the role of viscoelasticity needs to be investigated at depth in various cellular contexts. One such important context is cell migration. Cell migration is important in morphogenesis, immune response, wound healing, and cancer, to name a few. While it is known that cells migrate when presented with a substrate with a rigidity gradient, cellular behavior in response to viscoelastic gradient has never been investigated. The findings of this paper not only reveal a completely novel cellular taxis or directed migration, it also improves our understanding of cell mechanics significantly.