Nuclear Magnetic Resonance (NMR) T₂ inversion is the basis of NMR logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T₂ inversion result. We implemented both norm smoothing and curvature smoothing methods for NMR T₂ inversion, and compared the inversion results with respect to the optimal regularization parameters (α _opt) which were selected by the discrepancy principle (DP), generalized cross-validation (GCV), S-curve, L-curve, and the slope of L-curve methods, respectively. The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The α _opt selected by the L-curve method is occasionally small or large which causes an undersmoothed or oversmoothed T₂ distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more suitable for NMR T₂ inversion. The inverted T₂ distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.