This paper studies the influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained compound cylinder. 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 compound cylinder are made from high elastic compressible materials and their elasticity relations are given through the harmonic potential. The shear spring type imperfectness of the interface conditions is considered and the degree of this 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. In particular, it is established that as a result of the aforementioned imperfectness of the interface conditions, the dispersion curve related to the fundamental mode has two branches: the first disappears, but the second approaches the dispersion curve obtained for the perfect interface case by decreasing the shear-spring parameter.