The invention discloses a functional gradient thermal barrier coating quenching stress calculation method with a gradient index. Quenching stress generated in the preparation process of a functional gradient thermal barrier coating system with a gradient index is used; according to the substrate thickness hsub, the temperature Tsub, the melting point temperatures TmA and TmB of the equivalent elastic modulus substance A and the equivalent elastic modulus substance B, the equivalent elastic modulus and the thermal expansion coefficients alpha A and alpha B, the total thickness h and the gradient index p of the gradient coating are directly calculated to obtain the quenching stress sigma qi generated in the ith layer in the deposition process of the gradient coating, and the stress sigma sub-b-sigma i generated at the bottom of the substrate and stress sigma sub-t-sigma i generated at the top of the substrate. In addition, the final quenching stress of the gradient coating system can bedirectly calculated, and the evolution process of the quenching stress in the layer-by-layer deposition process of the gradient coating can also be calculated.