In this paper the author considers a Lorentzian manifold

$M$ carrying a time-like concircular unit vector field

$\xi $, that is a Lorentzian almost paracontact manifold with a structure of the concircular type. The notion first introduced by

*K. Matsumoto* [Bull. Yamagata Univ., Nat. Sci. 12, No. 2, 151–156 (1989;

Zbl 0675.53035)]. There are given conditions for such a manifold

$M$ to have

$\eta $-parallel Ricci tensor or to be

$\eta $-Einstein manifold and to admit constant scalar curvature. Additionally, some infinitesimal transformations on

$M$ are studied and the sectional curvature is obtained.