Creep crack growth (CCG) behaviors of 9Cr–1Mo heat resistant steel under different stress states, such as the different initial crack lengths, two/three dimensional stress states, different side groove depths and angles are investigated by the numerical method. The results show that decreasing the initial crack length can increase the specimen life. Affected by the higher stress tri-axiality in the specimen, the side groove specimen life is greater than that the plain CT specimen. Crack front straightness extent increases with the increasing of value of d/B0 or magnitude of the α. The side groove depth of d/B0 = 0.1 and side groove angle of α = 80° meet the crack front straightness requirement, and it can be used to predict the CCG rate of the 9Cr–1Mo steel. The CCG rate of the plane strain specimen is greater than that the plane stress specimen for both the same loading condition of initial stress intensity factor and reference stress. On the whole, all the CCG rate data are dropped into the 95% prediction band of fitting curve, demonstrating that the CCG rate of 9Cr–1Mo heat resistant steel can be reasonably calculated by C*.