This paper combines an X-Shaped structure with a linear spring and damping absorber to form a new X-Shaped absorber with both vibration dissipation and vibration isolation performance. Based on the Lagrange method, the dynamic equation of the single-degree-of-freedom linear oscillator coupled X-Shaped absorber system is established. The approximate analytical solution of the steady-state response of the system is obtained by the harmonic balance method, and the numerical solution obtained by the Runge-Kutta method verify the correctness of the analytical solution. The vibration reduction effect of the new X-Shaped absorber on the response amplitude and displacement transmissibility of the system for different excitations is discussed. In addition, the influence of different parameters on the amplitude-frequency response curve and displacement transmissibility of the system is analyzed. The results show that the new X-Shaped absorber can not only transform the linear stiffness into nonlinear stiffness, but also provide negative stiffness for the system, and has excellent vibration dissipation and ultra-low frequency vibration isolation performance.