In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in R n+1 , giving some conditions under which a translating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in R n+k , namely, if the L n norm of the second fundamental form of the soliton is small enough, then it is a hyperplane.Mathematics Subject Classification 2010: 53C21,53C44