In this paper, laminar flow of non-Newtonian (Bingham) fluid is studied numerically in a two-dimensional lid-driven skewed cavity that incorporates Papanastasiou exponential regularization approach of Bingham constitutive model [Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987), pp. 385–404]. Numerical simulation has been done using the finite-volume method with collocated grid arrangement. The governing equations including continuity and momentum are initially non-dimensionalized using appropriate transformation. To simulate irregular shape cavity flow problem, body-fitted non-orthogonal grids are used, and governing equations have been transformed to generalized curvilinear co-ordinates. In this study, two dimensionless parameters namely, Reynolds number and Bingham number are considered. A wide range of skew angles are considered which comprises both acute and obtuse angles. The obtained results are presented in terms of velocity and streamlines with yielded/unyielded region for different values of Bingham number and Reynolds number having different angles of the skewed cavity. The present results may be serve as benchmark results for comparison purpose in the case of non-Newtonian (Bingham) fluid flow.