In this talk, we discuss the soft-gluon resummation for a pair of Higgs bosons in the dominant gluon fusion channel to next-to-next-to-next-to-leading logarithmic (N$^3$LL}) accuracy. Through the study, we achieve sub-percent level accuracy in the uncertainties from the residual renormalisation and factorisation scales, for both inclusive and differential mass distribution in the infinite top quark mass limit. We also combine these results with the full top mass dependent next-to-leading order calculations.