The phase diagrams and compensation behaviors of a mixed spin (1/2-1) hexagonal Ising nanowire with core-shell structure are studied by using the effective-field theory with correlations. The effects of the interaction parameters and crystal field on the critical behaviors of the system are investigated, in detail. It has been found that the system shows first-order and second order phase transition, and tricritical point. Moreover, Q-, R-, S- and N-types of compensation behaviors in the Neel classification nomenclature as well as reentrant behaviors are observed in the system. (C) 2013 Elsevier Ltd. All rights reserved.