We compute the two-loop Higgs plus three partons amplitudes with high dimensional operators in Higgs effective theory. This provides the two-loop S-matrix elements for the top mass corrections for Higgs plus a jet production at LHC. The results take remarkably simple analytic form. In particular, the maximally transcendental part (functionally the most complex part) presents hidden relations and universal structure. In this talk, I will give an introduction to the related background and also explain the method used to obtain the results.