Abstract: Symmetry group classifications of variable coefficient mKdV equation is performed by using the classical infinitesimal Lie method, the technique of equivalence transformations and the theory of classification of abstract lowdimensional Lie algebras. It is shown that there are four and six inequivalent mKdVtype nonlinear evolution equations admitting one and two-dimensional solvable Lie algebras, respectively. Furthermore, we prove that there exist no equation admitting three- and higerdimensional Lie algebras.