One of the main characteristic parameters of the polaron is its effective mass, which can be determined from the experiments on the cyclotron and magneto-phonon resonance. The aim of the present study is to theoretically investigate the influence of the screening effect of electron longitudinal-optical (LO) phonon interaction on weak coupling Fröhlich polaron mass in semiconductor hollow nanocylinder (HNC). General analytical expressions for the polaron mass have been obtained in arbitrary values of HNC radius 0 r taking into account screening as well as considering transitions between subbands of dimensional quantization within the framework of the standard perturbation theory. The dependence of the polaron mass for ground and excited states on nanocylinder radius has been obtained on the basis of numerical calculations. The calculation is carried out within the framework of the standard perturbation theory. According to research carried out, it has been established that the screening contribution to the correction of the polaron mass taking into account the virtual transitions from the ground state to subbands n = ±1, ±2, ±3, as well as the transitions from the polaron excited state with n = 1 to subbands n = −1, ±2, ±3, is significant for = 0 < 1 p a r r values, where p L r =  2mω is the polaron radius, L ω is the limiting LO phonon frequency.For values of the parameter a > 1 the screening contribution to polaron mass decreases with increasing nanocylinder radius, but the decrease of the polaron correction to the mass due to screening is still more than 30 %. In particular, the results of numerical calculations of specific case for dependences ( Δm mα ) on the ratio p r r 0 are presented in figurefigureFig. Dependence of Δm mα on the p r r 0 ratio taking into account transitions from ground band state with n = 0 to subbands n = ±1, ±2, ±3: a) solid curve is obtained without taking into account screening, b) dotted curve - with taking into account screening. Fermi level is placed in the zero band As seen from solid curve of this figure the value of Δm mα was approached to its well known value of π 8 with increasing the value of the NC radius p r r 0 . Here p Δm = m − m ; where m , p m - effective electron and polaron masses;α is the electron-phonon coupling parameter.