The present study focuses on to explore the dynamic analysis of a viscoelastic propeller-shaft system with transverse breathing crack supported by journal bearings. Finite element modelling of the shaft continuum is done considering the Euler-Bernoulli beam theory. Operator based constitutive relationship isapplied to incorporate material damping of the rotor and higher-order equations of motion are established.Accurate time-dependent functions are used to formulate cracked element stiffness matrix and augmented to the overall stiffness matrix of the entire system. Eigen analysis is performed after converting the higher-order equation into the first-order form. A Comparative study is demonstrated based on different dynamic parameters like whirl frequency, modal damping factor and stability limit of spin speed. Further, the variation of stabilitylimit of spin speed and natural frequency is also studied based on the parameters such as crack depth and its location along different section of the propeller shaft.