A new class of generalized nonlinear set-valued variational inclusions involving H-monotone mapping are introduced and studied. By using the properties of the resolvent operator associated with a H-monotone mappings in Hilbert spaces. An existence theorem of solution for the generalized nonlinear set-valued variational inclusions involving H-monotone mappings is established and a new algorithn is constructed. The author proves the iterative sequences generated by the algorithm strongly converge to its exact solution. Our results improve and generalized known corresponding and results.