Data　sparseness　brings　significant　challenges　to　the　research　of　recommender　systems.　It　becomes　more　severe　for　neighborhood-based　collaborative　filtering.　We　introduce　the　trust　relation　computing　of　the　sociology　field.　Instead　of　the　traditional　similarity　computing　method,　the　trust　degree　is　integrated　for　the　nearest　neighbor　selection.　The　trust　network　is　constructed　by　the　expansion　of　different　path　length,　and　the　trust　value　between　the　users　can　be　obtained　by　the　trust　transmission　rules.　To　verify　the　effectiveness　of　our　method,　we　give　the　experiments　on　different　techniques　for　rating　prediction,　including　Pearson　based　method,　the　User　position　similarity　(UPS)　based　method　and　the　trust　with　Pearson　and　UPS.　We　also　give　the　t-test　result.　The　implementation　of　the　experiment　on　the　Epinions　data　set　shows　that　the　proposed　method　can　improve　the　system　performance　significantly.