In　this　paper,　we　propose　a　new　customized　proximal　point　algorithm　for　linearly　constrained　convex　optimization　problem,　and　further　extend　the　proposed　method　to　separable　convex　optimization　problem.　Unlike　the　existing　customized　proximal　point　algorithms,　the　proposed　algorithms　do　not　involve　relaxation　step,　but　still　ensure　the　convergence.　We　obtain　the　particular　iteration　schemes　and　the　unified　variational　inequality　perspective.　The　global　convergence　and　O(1/k)-convergence　rate　of　the　proposed　methods　are　investigated　under　some　mild　assumptions.　Numerical　experiments　show　that　compared　to　some　state-of-the-art　methods,　the　proposed　methods　are　effective.