We have studied the Rashba spin-orbital effect on a semiconductor hollow nanocylinder with finite wall thickness in the presence of a magnetic field parallel to the nanocylinder axis. The wall thickness of nanocylinder is modeled by means of a parabolic potential. We have obtained an analytical expression for the electron energy spectrum, when the wall thickness of nanocylinder is small compared to nanocylinder radius. It has been shown that the interplay of Rashba effect, magnetic and electric field strongly changes the electron spectrum of a nanocylinder with finite wall thickness, yielding multivalley energy dispersion in each quantized subband. The results are used to obtain the conductance of the nanocylinder at finite temperature. It is shown that the presence of additional local extremum points in the subbands of the electronic spectrum leads to a nonmonotonic dependence of the ballistic conductance of the system on the chemical potential and magnetic field. In the presence of magnetic field with taking into account the Rashba splitting, each minimum of subband contributesG0 2 (where 2 0 G = 2e h is the conductance quantum) to conductance and each local maxima in the subband actually reduce the conductance by 0 G 2 . The effect of finite temperature on the DMS cylinder conductance is a smearing out the sharp steps in the zero-temperature conductance.