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 Exact solutions for a Dirac-type equation with N-fold Darboux transformation Qiulan Zhao,Jinting Ha,Huiqun Zhang Keywords:Dirac-type equation, the Lie algebra so(3,$\mathbb{R}$), Darboux transformation, exact solutions. Abstract: Based on matrix spectral problems associated with the real special orthogonal Lie algebra so(3,$\mathbb{R}$), a Dirac-type equation is derived by virtue of the zero-curvature equation. Further, a N-fold Darboux transformation for the Dirac-type equation is constructed by means of the gauge transformation. Finally, as its application, some exact solutions and their figures are obtained via symbolic computation software (Maple).