A theoretical treatment of mode I crack problem is put forward for a functionally graded orthotropic strip. The internal crack and edge crack perpendicular to the boundaries are investigated, respectively. The elastic property of the material is assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. The singular integral equation for solving the problem and the corresponding asymptotic expression of the singular kernel are obtained. Three different loading conditions, namely crack surface pressure, fixed-grip loading and bending, are considered during the analysis. The influences of parameters such as the material constants and the geometry parameters on the stress intensity factors (SIFs) are studied.