Abstract: The authors  introduce    and  study   a  new  class  of  generalized   mulit-valued  variational-like  inclusions  with  (G,η)-monotone  mappings  in  Hilbert  spaces.By  using  the  resolvent operator associated with (G,η)-monotone mappings,an  existence  theorem  of  solutions  for  this  kind  of  variational  inclusions  is estaslished  a  new approximation  algorithm is suggested,and  the  convergence  of  iterative  sequences  generated  by  the algorithm is proved.The results presented in this paper generalize,improve,and unify some recent results  in this field.

Key words: generalized   , mulit-valued   , variational-like , inclusions;(G,η)-monotone mapping;resolvent operator;approximation algorithm;convergence