In　this　paper,　the　optimal　H2model　order　reduction　(MOR)　problem　for　bilinear　systems　is　explored.　The　orthogonality　constraint　of　the　cost　function　generated　by　the　H2MOR　error　makes　it　is　posed　not　on　the　Euclidean　space,　but　can　be　discussed　on　the　Stiefel　manifold.　Then,　the　H2optimal　MOR　problem　of　bilinear　systems　is　turned　into　the　unconstrained　optimisation　on　the　Stiefel　manifold.　The　explicit　expression　of　the　gradient　for　the　cost　function　on　this　manifold　is　derived.　Full　use　of　the　geometry　properties　of　this　Stiefiel　manifold,　we　propose　a　feasible　and　effective　iterative　algorithm　to　solve　the　unconstrained　H2minimisation　problem.　Moreover,　the　convergence　of　our　algorithm　is　rigorously　proved.　Finally,　two　practical　examples　related　to　bilinear　systems　demonstrate　the　effectiveness　of　our　algorithm.　©　2017　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group