The fracture problem of the functionally graded material with collinear cracks under the condition of different elasticity moduli. The stress fields and displacement fields of cracks in the functionally graded strip can be obtained by means of the method of integral transform. And solving the problem of cracks is equivalent to solving the problem of singular integral equations combined with boundary conditions and continuity conditions after solving the stress fields and displacement fields of each crack. The stress intensity factors can be obtained after solving the singular integral equations. The effects of elasticity moduli of materials and geometric parameters of cracks on SIFs are discussed. The results show that the distribution of elasticity moduli may affect SIFs significantly. And this study can provide scientific basis for forming FGMs and designing the property distribution in FGMs.