The classification of three-dimensional real Lie algebra was completed according to the properties of derivative algebras and isomorphic conditions of Lie algebra. When the dimension of derivative algebra is 0 or 1, Lie algebra can be divided into three types, $ L\left( {3,0} \right)$, $ L\left( {3, - 1} \right)$ and $ L\left( {3,1} \right)$, according to the properties of Lie bracket operation and the transformation of basis.When the dimension of derivative algebra is 2 or 3, Lie algebras can be divided into five types, $ L\left( {3,2,a} \right)$, $ L\left( {3,3} \right)$, $ L\left( {3,4,c} \right)$, $ L\left( {3,5} \right)$, $ L\left( {3,6} \right)$, according to the properties of eigenvalues of matrix corresponding to internal derivations.