We　consider　the　backward　heat　equation　u(xx)(x,　t)　=　u(t)(x,　t),　-infinity　＜　x　＜　infinity,　0　＜=　t　＜　T.　The　solution　u(x,　t)　on　the　final　value　t　=　T　is　an　known　function　g(T)(x).　This　is　a　typical　ill-posed　problem,　since　the　solution　-　if　it　exists　-　does　not　depend　continuously　on　the　final　data.　In　this　paper,　we　shall　give　a　Shannon　wavelet　regularization　method　and　obtain　some　quite　sharp　error　estimates　between　the　exact　solution　and　the　approximate　solution　defined　in　the　scaling　space　V-j.　(C)　2011　Elsevier　B.V.　All　rights　reserved.