An Incompressible Navier-Stokes solver using the Entropically damped artificial compressibility (EDAC) method is developed. The original EDAC method is recast into the generalized curvilinear coordinates to enhance its capability to handle complex geometries. The resulting system of equations in the computational space are solved using the high-order finite difference schemes. The solver is validated on several steady/unsteady benchmark cases at low and high Reynolds numbers which include: Taylor Green Vortex, doubly periodic shear layer, and Invis-cid convecting vortex. High-order schemes with EDAC method have shown superior accuracy when compared to the low-order schemes, even on highly distorted and dynamically deforming meshes. In addition, conservative form of metrics for dynamically deforming meshes has shown to considerably reduce the metric cancellation errors. Due to the hyperbolic-parabolic nature of governing equations, the high order EDAC solver in curvilinear coordinates is faster and highly scalable than the elliptic methods and has a comparable accuracy to the conventional projection-based methods. © 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.