This paper studies the dispersion of the axisymmetric longitudinal wave propagation in the pre-strained hollow cylinder consisting of two-layers under the shear-spring type imperfectness of the contact conditions between these layers. The investigations are made within the framework of the piecewise homogeneous body model by utilizing the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the layers of the cylinder are made from compressible hyper-elastic materials and their elasticity relations are given through the harmonic potential. The degree of the mentioned imperfectness is estimated by the shear-spring parameter. Numerical results on the influence of this parameter on the behavior of the dispersion curves related to the fundamental mode are presented and discussed. It is established that the considered type imperfectness of the contact conditions causes two branches of the dispersion curve related to the fundamental mode to appear: the first disappears, but the second approaches the dispersion curve obtained for the perfect interface case by decreasing the shear-spring parameter.