Abstract: An improvement of Hardy-Hilbert’s inequality can be obtained by means of a sharpening of Hlder’s inequality,a newinequality of the form  ∞n=0∞m=0(ａｍｂｎ/(（２ｍ＋１）λ＋（２ｎ＋１）λ)＜π/(２λｓｉｎ（π／ｐ）)｛∞m=0（２ｍ＋１）ｐ－１－λａｐｍ｝１/ｐ｛∞n=0（２ｎ＋１）ｑ－１－λｂｑｎ｝１/ｑ（１－Ｒ）ｋis built.

Key words:  Hardy-Hilbert inequality；Hlder inequality；&beta, function