In this note, the generalized Lorentzian Sasakian-space-form M 1 2 n + 1 (f 1 , f 2 , f 3) satisfying certain constraints on the M -projective curvature tensor W * is considered. Here, we characterize the structure M 1 2 n + 1 (f 1 , f 2 , f 3) when it is, respectively, M -projectively flat, M -projectively semisymmetric, M -projectively pseudosymmetric, and φ − M -projectively semisymmetric. Moreover, M 1 2 n + 1 (f 1 , f 2 , f 3) satisfies the conditions W * (ζ , V 1) · S = 0 , W * (ζ , V 1) · R = 0 and W * (ζ , V 1) · W * = 0 are also examined. Finally, illustrative examples are given for obtained results. [ABSTRACT FROM AUTHOR]