This　paper　presents　a　new　Riemannian　modified　Polak-Ribiére-Polyak　conjugate　gradient　algorithm　to　construct　the　reduced　systems　of　quadratic-bilinear　systems.　We　eliminate　the　orthogonality　and　homogeneity　constraints　of　the　truncated　H　2　optimal　model　order　reduction　problem　and　turn　this　constrained　minimization　problem　into　an　unconstrained　Riemannian　optimization　problem　on　the　Grassmann　manifold.　Due　to　the　compactness　of　this　manifold,　the　existence　of　the　minimum　solution　can　be　guaranteed.　Applying　tensor　techniques,　the　Riemannian　gradient　of　the　cost　function　is　derived.　Additionally,　we　design　a　new　Riemannian　MPRP　conjugate　gradient　scheme　using　the　differentiated　retraction　and　the　scaled　vector　transport.　The　resulting　search　direction　always　provides　a　descent　direction.　The　global　convergence　of　the　proposed　algorithm　is　established.　Moreover,　our　algorithm　is　also　applicable　to　the　minimization　problems　of　linear　and　bilinear　systems.　Finally,　two　numerical　tests　are　reported　to　illustrate　the　effectiveness　of　the　proposed　algorithm.　©　2020　Society　for　Industrial　and　Applied　Mathematics