This paper presents an approach with a modified M-integral for determining the stress intensity factors of cracked functionally graded titanium alloy (FGTA) components. A derivative term of the strain energy density with respect to the spatial coordinate is embedded in the modified M-integral to account for the effect of the varying elastic moduli of functionally graded material. The validity of the modified M-Integral is validated by comparison with the experimental results of the crack propagation of FGTA specimens that are manufactured by using three-dimensional (3D) printing. Resistance tests of the cracked FGTA specimens are simulated to investigate the effects of the controlled changes in the material properties on the residual strength and crack-tip stress intensity factor. Further simulations of the fatigue crack propagation of the cracked FGTA specimens are performed to examine the influence of the changes in the material properties on the fatigue crack propagation life and crack propagation rate. The analysis results indicate that the numerical method in this study can accurately simulate the crack propagation of FGTA specimens. At present, due to the complexity and limitations of additive manufacturing of materials with gradient variations, it is not available to manufacture fully graded components through 3D printing for experiments. Therefore, this study assumes an FGTA beam model that is a fully graded material model to examine the effect of material gradient on crack propagation.