The concept of Teichmuller space of a Fuchsian group can be extended to any non-discrete group of conformal isometries of the hyperbolic plane. Let G be a non-discrete subgroup of PSL(2;R). We show that the Teichmuller space T(G) of G is not trivial if and only if G is a non-discrete consisting of hyperbolic elements with two common fixed points. Furthermore, we show that if T(G) is not trivial, then (i) T(G) is conformally equivalent to a unit disk; (ii) the length spectrum is just a pseudometric, but it is a metric coinciding with the Teichmuller metric when restricted on a one-dimensional slice. This is a joint work with Francisco G. Jimenez-Lopez.