The β-functions and the c-function are calculated in a two-dimensional field theory where the coupling parameters are functions of fields. The action of the theory is given by a combination of the Polyakov action for string theory and the Zamolodchikov action for the deformation of conformal field theory. The c-function is written as the Landau-Ginzburg type action in terms of the coupling parameter functions. The linear β-functions near fixed points are given by the Klein-Gordon equation. The corresponding well-defined masses are calculated.