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.