This paper describes a novel gradient smoothing method (GSM) and its application for solutions to steady-state and transient incompressible fluid flow problems. The proposed method is based on irregular cells and thus can be used for problems with arbitrarily complex geometrical boundaries. Strong form of incompressible Navier-Stokes equations enhanced with artificial compressibility terms are tackled, in which the spatial derivatives are approximated by consistent and successive use of gradient smoothing operation over smoothing domains at various locations. A favorable GSM scheme corresponding to a compact stencil with positive coefficients of influence have been derived and adopted throughout this study. Pseudo-time advancing approach is used for solving the augmented governing equations with mixed hyperbolic-parabolic properties. The dual time stepping scheme and point-implicit five-stage Runge-Kutta (RK5) method are implemented to enhance the efficiency and stability in iterative solution procedures. The proposed incompressible GSM solver has been tested for solutions to some classical benchmarking problems, including steady-state flows over a back step, within a lid-driven cavity and across a circular cylinder, and unsteady flow across the circular cylinder. Alike to the compressible GSM solver, the incompressible GSM solver exhibits its robust, stable and accurate behaviors amongst all the testing cases. The attained incompressible GSM solutions show perfect agreements with experimental and literature data. Therefore, the proposed GSM can be reliably used for accurate solutions to versatile fluid flow problems.