We propose a new approach to deriving the local three-dimensional (3D) non-force free coronal magnetic field structure from photospheric vector magnetograph measurements. Based on the Principle of Minimum Dissipation Rate, a general non-force free magnetic field can be expressed as the superposition of two linear (constant-α) force free field. The parameter, α, for each of the two linear force free field, can be determined by optimizing the requirement that the recovered transverse magnetic field components as the superposition of the corresponding components of the two linear force free field agree with the observed ones at the photospheric level. A preliminary test case study of an analytic non-force free field model is presented to illustrate the method. We discuss the difficulties associated with the linear force free field extrapolation and the feasibility of our method.