The magnetic properties of a cylindrical Ising nanotube with a spin-1/2 core surrounded by a spin-3/2 shell system have been studied by means of the effective field theory (EFT). We have investigated the effects of crystal-field coupling at the surface shell and bilinear interactions among the core and surface shells to the order parameters, susceptibility, internal energy, specific heat, and free energy. Some characteristic phenomena are examined in terms of thermal or crystal-field variations when the other system parameters are fixed. Moreover, we have observed first-order and second-order transitions and critical end points in the (D/J, kT/J) plane, where D/J and kT/J are crystal-field and temperature, respectively. (c) 2014 Elsevier B.V. All rights reserved.