In the present study, magnetization and dispersion relations of spin-waves propagating along a segmented nanotube constructed of atomic layers of ferromagnetic and non-magnetic materials are considered by use of the Green function method. Within the framework of random-phase approximation, the expression of Green functions for different spins of segmented nanotubes, which is modeled as having a hexagonal cross section are derived. The effects of the composition (p) and exchange couplings on spin-wave spectra and temperature dependence of magnetization are investigated in detail. It was found that small magnetization is observed in the system at small values of parameter p and exchange constants, and the critical temperature at which second-order phase transition occurs is low. When the obtained theoretical results compare with some other works, a very good agreement between them is observed.