In this paper, the superposition model (SM) and complete diagonalization procedure of energy matrix (CDM method) were used for a few selected Nd3+ (4f3) paramagnetic centers with trigonal symmetry in congruent lithium niobate (LN, LiNbO3) single crystals. Additionally, the g-shift method was applied to these systems. In general, the calculated g-factors (parallel and perpendicular) match the measured values very well. The displacements of the Nd3+ ions calculated by g-shift method are also fit very well to the experimental values. A detailed structural analysis of paramagnetic Nd3+ centers with trigonal symmetry in congruent LN single crystals was also performed. The charge compensation mechanism and its role in establishing Nd3+ centers in congruent LN are also debated.