Neyman-Pearson　classification　has　been　studied　in　several　articles　before.　But　they　all　proceeded　in　the　classes　of　indicator　functions　with　indicator　function　as　the　loss　function,　which　make　the　calculation　to　be　difficult.　This　paper　investigates　Neyman-Pearson　classification　with　convex　loss　function　in　the　arbitrary　class　of　real　measurable　functions.　A　general　condition　is　given　under　which　Neyman-Pearson　classification　with　convex　loss　function　has　the　same　classifier　as　that　with　indicator　loss　function.　We　give　analysis　to　NP-ERM　with　convex　loss　function　and　prove　it＇s　performance　guarantees.　An　example　of　complexity　penalty　pair　about　convex　loss　function　risk　in　terms　of　Rademacher　averages　is　studied,　which　produces　a　tight　PAC　bound　of　the　NP-ERM　with　convex　loss　function.　©　2008　Editorial　Board　of　Analysis　in　Theory　and　Applications　and　Springer-Verlag　GmbH.