Abstract: High-order λ harmonics have valuable applications in the fields of core power re-construction, re-fueling optimization and neutron characteristics study of ADS sub-critical reactor. To calculate high-order λ harmonics, based on the implicitly restarted Arnoldi method (IRAM), the HARMONY code for arbitrary high-order λ eigenvalue and harmonics calculation in one, two and three Cartesian coordinates neutron diffusion equation was developed and verified by the benchmark problems. The results indicate that HARMONY code is capable for high-order λ eigenvalue calculation and has good numerical accuracy. It can be applied in future for λ harmonics based neutron characteristics study of ADS sub-critical reactor.