The alkaloid carbazole is one of the relevant structural motifs in drug discovery. Indeed, carbazoles have been largely investigated for their various biological properties. In this article, in order to ensure the possibility of carrying out the carbazole N-alkylation synthesis reaction at the synthesis laboratory level and to gain access to a new active biomolecule, we present the theoretical study of strategies for the synthesis of an N-alkylcarbazole using the DFT method at B3LYP, with the basis set 6-31G(d,p). In fact, this research has enabled us to establish a simple, economic, and efficient synthesis strategy for this nitrogenous heterocycle with an excellent yield, by N-alkylation between carbazole and propargyl bromide under different experimental conditions. We have developed an environmentally respectful synthesis process, a gentle packaging protocol and a practical procedure for the preparation of this polycyclic aromatic compound. The structure of the synthesized compound was determined by spectroscopic methods: 1H-NMR, 13C-NMR, and MS data. The theoretical results corroborate with experiences. The study of the substitution effect on the optical properties of reagents and products shows that N-alkylation has an influence on the optical properties.