Deformed on the basis of the Voigt vibration absorber， a grounded stiffness vibration absorber is presented， and an im proved method based on the fixed-point theory is proposed to calculate the closed-form solution of the fixed-point coordinates of the system. Analytical and numerical methods are used to study the maximum amplitude of primary system response， and global opti mization is performed according to the fixed-point amplitude characteristics. The design formulas for the optimal natural frequency ratio and the optimal damping ratio are derived. Numerical simulation is used to verify the correctness of the analysis. Under the ex citation of harmonic force， compared with the local and global optimized Voigt vibration absorber and grounded damper vibration absorber， it is found that the response peak of the grounded stiffness vibration absorber after the global optimization is consistent with the grounded damper vibration absorber. Both are smaller than the global optimized peak value of Voigt vibration absorber and the local optimized peak value of grounded damper vibration absorber. The vibration damping bandwidth of the grounded stiffness vibration absorber is the largest. Compared with the grounded damper vibration absorber after global optimization， the grounded stiffness vibration absorber has better vibration damping performance in the vibration damping frequency band of the grounded damper vibration absorber. And the mass of the subsystem required to achieve the common damping ratio is much smaller.