Abstract: For the higher eigenmodes of neutron transport/diffusion forward and adjoint equations, there are various application perspectives for engineering purposes, such as core power distribution reconstruction, stability analysis, and uncertainty and sensitivity analysis. In this paper, the higher eigenmodes of both forward and adjoint equations are calculated using implicitly restarted Arnoldi method（IRAM） based on domain decomposition parallel computation and multi-group multi-domain coupled PGMRES accelerating algorithm. The IAEA3 D diffusion benchmark, a 1 D 2-group 2-domain transport problem and 2 D C5 G7 benchmark are used for verification. Numerical results demonstrate that the forward equations and the adjoint equations keep the same eigenvalue spectrum, and the obtained higher eigenfunctions are F-orthogonal or biorthogonal. These numerical results agree well with the expectations of theory analysis.