Mode III fracture failure of a through crack in an orthotropic functionally graded strip is investigated. The shear moduli in two directions of the material are respectively assumed to vary proportionately as a definite gradient. Fourier cosine transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Energy density factor criterion is applied to obtain the maximum of the minimum energy density and direction of crack initiation. Numerical results are given graphically to illustrate the effects of the material property parameters and geometry criterion on the energy density factor.