Let ($M^3$, $g$) be a 3-dimensional closed Sasakian spin manifold. Let $S_{min}$ denote the minimum of the scalar curvature of ($M^3$, $g$). Let ${lambda}^+_1$ > 0 be the first positive eigenvalue of the Dirac operator of ($M^3$, $g$). We proved in [13] that if ${lambda}^+_1$ belongs to the interval ${lambda}^+_1{in}({frac{1}{2}},;{frac{5}{2}})$, then ${lambda}^+_1$ satisfies ${lambda}^+_1{geq}{frac{S_{min}+6}{8}}$. In this paper, we remove the restriction "if ${lambda}^+_1$ belongs to the interval ${lambda}^+_1{in}({frac{1}{2}},;{frac{5}{2}})$" and prove $${lambda}^+_1{geq};{frac{S_{min}+6}{8};for;-frac{3}{2}<S_{min}{leq}30, \{frac{1+sqrt{2S_{min}}+4}{2}};for;S_{min}{geq}30$$.