The purpose of the present paper is the study of CR-submanifolds of a nearly trans-Sasakian manifold with a quarter symmetric non-metric connection and obtain their basic properties. Nijenhuis tensor is calculated and integrability conditions of the distributions D and  of CR-submanifolds of a nearly trans-Sasakian manifold with a quarter symmetric non-metric connection are obtained.

CR-submanifolds, nearly trans-Sasakian manifold, quarter symmetric non-metric connection, distributions, integrability conditions.