An almost contact metric manifold is called trans-Sasakian if
and being certain functions on [J. A. Oubina, Publ. Math. 32, 187- 193 (1985; Zbl 0611.53032)]. In this paper, CR-submanifolds of such manifolds are investigated. The conditions under which the distributions required by such manifolds are integrable are stated. -parallel normal sections as well as totally umbilical CR-submanifolds are also studied.