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The suppression of lift oscillation of flow past a stationary circular cylinder is studied to delay structural fatigue at low Reynolds numbers in incompressible Newtonian fluid. Grad-based shape optimization is employed to achieve the goal. The optimization objective is the integral of the absolute value of the lift coefficient over a vortex shedding period T. The class-shape function transformation technique is chosen as a shape parameterization method. Moreover, the unsteady adjoint method is employed to calculate the gradients of the objective with respect to shape parameters. Results show that through shape optimization, the strength of vortex shedding is sufficiently suppressed in two-dimensional flow, and the lift oscillation amplitude is reduced by nearly 50%. In addition, the flow stability is significantly improved, and the lift oscillations are completely eliminated at Re = 47–60. [ABSTRACT FROM AUTHOR]