In this paper, we exploit the Lie group method to analyse the group-invariant solutions of a new kind of hyperbolic geometric flow-dissipative hyperbolic geometric flow. By constructing the optimal systems of one-dimensional subalgebras, our goal is to perform the similarity reductions and obtain exact solutions of dissipative hyperbolic geometric flow. Then the explicit solutions are constructed by the power series method. Moreover, the convergence of the power series solutions is discussed.

dissipative hyperbolic geometric flow, symmetry reduction, optimal system, power series solutions.