In this paper, we have studied the magnetic properties of the nanotube core-shell structure with RKKY (Ruderman-Kittel-Kasuya-Yosida) interactions, using Monte Carlo simulations (MCS). The system consists of hexagonal core-shell nanotube structure with mixed spins σ = ± 3/2, ± 1/2 (of the core) and S = ±1, 0 (of the shell), separated by non-magnetic nanotubes. Initially, we start this study by discussing for zero temperature, the ground-state phase diagrams in different planes. Moreover, we investigate for the positive temperature values, the effect of the RKKY interactions on the thermal magnetization and magnetic susceptibility of the system. Additionally, we study the effects of the exchange coupling interactions of the core and of the shell on the compensation and transition temperatures. Finally, we explore the behavior of the magnetic hysteresis cycles as a function of the non-magnetic nanotubes number, the temperature, and the exchange coupling parameters.