Grain orientation dispersion in polycrystals is a key factor contributing to the fatigue crack initiation life dispersion. However, there is a lack of quantitative research on the effect of grain orientation dispersion on fatigue crack initiation life in polycrystals, which leads to the unclear impacts of grain orientation dispersion on fatigue crack initiation. In this paper, the effect of grain orientation dispersion on fatigue crack initiation in polycrystals is quantitatively analysed using a combination of theoretical and numerical simulations for Ni-based powder superalloy FGH96. The FGH96 exhibits low texture strength, with grains oriented randomly. 500 finite element models are created, each featuring a grain region with a distinct grain orientation distribution to ensure diversity and randomness in grain orientations. Finite element simulations using a crystal plasticity model are conducted under cyclic uniaxial tension. The slip system activity and crack initiation sites are analysed. A quantitative analysis of the effect of grain orientation dispersion on \(FI{P}^{\alpha }\) is achieved and a characterisation of fatigue crack initiation life in polycrystals considering grain orientation dispersion is established.