In　this　paper,　we　discuss　the　structure-preserving　H2　optimal　model　order　reduction　(MOR)　problem　of　integral-differential　systems　based　on　the　projection　technique.　Different　from　the　common　idea,　we　take　a　new　way　to　deal　with　this　minimization　problem　and　for　the　first　time　reduce　the　integral-differential　systems　on　the　product　of　two　Stiefel　manifolds.　The　cost　function　is　viewed　as　a　function　whose　parameters　are　a　pair　of　projection　matrices　with　different　dimensions,　and　then　the　H2　optimal　MOR　problem　is　reformulated　as　the　minimization　problem　of　the　product　of　two　Stiefel　manifolds.　We　extend　the　Riemannian　geometry　of　the　single　Stiefel　manifold　to　the　product　manifold　and　the　Riemannian　gradient　of　the　cost　function　is　derived　using　the　orthogonal　projection　of　the　product　manifold.　Further,　we　design　a　Riemannian　conjugate　gradient　scheme　on　the　product　manifold,　and　propose　a　structure-preserving　Riemannian　conjugate　gradient　algorithm.　The　resulting　search　direction　is　a　descent　direction　of　the　cost　function.　Besides,　we　show　that　our　algorithm　is　globally　convergent　and　has　the　potential　application　to　second-order　systems.　Finally,　numerical　examples　demonstrate　the　effectiveness　of　the　proposed　algorithm.　©　2022　The　Franklin　Institute