In this paper, we presented the quasi-static characteristics of novel microstrip lines with anisotropic grooved dielectric in finite metal. A quasi-static mode-matching method has been used to analyze this new structure and the simulation results are validated through comparison with other available results. The results in this paper show that it is possible to control the propagation characteristics of microstrip lines with the use of anisotropic grooved dielectric in finite metal. Also anisotropic grooved dielectric in microstrip line can be newly added to the design parameters of high performance three dimensional monolithic microwave circuits and other microwave applications.