Linear stability theory is used to analyze the stability of the basic state solution of Marangoni convection in a liquid bridge with liquid encapsulation. By processing the linear disturbance equations numerically, stability analysis can be evolved to a complex general eigenvalue problem. Inverse iteration algorithm combined with LZ algorithm is employed to solve the complex generalized eigenvalue problem. The results show that the stability of the system can be enhanced greatly by choosing reasonable matching parameters of the two fluid layers. The preferred mode of instability is axial wave number alpha = 2, 3 and 4, which means that the system is more sensitive to the disturbance with larger wave lengths.