To function efficiently in the body, the biological cells must have the ability to sense the external environment. Mechanosensitivity toward the extracellular matrix was identified as one of the sensing mechanisms affecting cell behavior. It was shown experimentally that a fibroblast cell prefers locomoting over the stiffer substrate when given a choice between a softer and a stiffer substrate. In this article, we develop a discrete model of fibroblast motility with substrate-rigidity sensing. Our model allows us to understand the interplay between the cell-substrate sensing and the cell biomechanics. The model cell exhibits experimentally observed substrate rigidity sensing, which allows us to gain additional insights into the cell mechanosensitivity.