A　novel　family　of　isoparametric　bilinear　finite　volume　element　schemes　are　constructed　and　analyzed　to　solve　the　anisotropic　diffusion　problems　on　general　convex　quadrilateral　meshes.　These　new　schemes　are　obtained　by　employing　a　special　quadrature　rule　to　approximate　the　line　integrals　in　classical　Q(1)　-finite　volume　element　method.　The　new　quadrature　rule　is　a　linear　combination　of　trapezoidal　and　midpoint　rules,　and　the　weights　depend　on　a　parameter　omega(K).　The　novelty　of　this　work　is　that,　for　any　fully　anisotropic　diffusion　tensor,　we　provide　some　specific　omega(K)　to　ensure　the　coercivity　result　of　the　proposed　schemes　on　arbitrary　parallelogram,　quasi-　parallelogram,　trapezoidal　and　some　general　convex　quadrilateral　meshes.　More　interesting　is　that,　the　parameter　omega(K　)can　only　involves　the　anisotropic　diffusion　tensor　and　the　geometry　of　quadrilateral　cell.　An　optimal　H(　)(1)error　estimate　is　also　proved　on　quasi-parallelogram　meshes.　Finally,　the　theoretical　findings　are　validated　by　several　numerical　examples.