In this article, a novel alpha gradient smoothing method (αGSM) based on the strong form of governing equations for fluid problems is presented. The basic principle of αGSM is that the spatial derivatives at a location of interest are approximated by the gradient smoothing operation. The main difference among the piecewise-constant gradient smoothing method (PC-GSM), piecewise-linear gradient smoothing method (PL-GSM), and αGSM is the selection of smoothing function. In the αGSM, the α value controls the contribution of the PC-GSM and PL-GSM. The αGSM is also verified by the solving the Poisson equation. The proposed αGSM has been tested for one benchmark example. All the numerical results demonstrate that the αGSM is remarkably accurate, robust, and stable. Finally, the αGSM has been applied to analyze the flow characteristic in the diseased artery in terms of stenosis.