We investigate the effect of a transverse field on a cylindrical core/shell spin-1 Ising nanowire, within the effective-field theory based on a probability distribution technique, in order to clarify how the relevant thermodynamic quantities such a magnetizations, hysteresis loops, compensation behaviors, are influenced by a transverse field. From these studies, following interesting phenomena are found. (i) Beside a singly hysteresis loop, double, triple or even quadruple hysteresis loops occurs in the system. (ii) The P and N types of compensation behavior are obtained in addition to the Q-, R- and S-types. We also compare our results with some experimental and theoretical results and find in a qualitatively good agreement.