The models of the true secondary electron emission and backscattered electron emission for metal are provided, based on the physical process of secondary electron emission from metal at high incident electron energy. The formula for the true secondary electron yield at high incident electron energy is derived with the Bethe equation known to provide accurate and simple analytical expressions for the stopping power and the probability that a secondary electron produced in a material reaches the surface and is emitted into the vacuum. The formula for the backscattered electron yield at high incident electron energy is derived with the absorbing rule for the incident electron in the material. All the above results lead to a new model for secondary electron emission from metal at high incident electron energy. The secondary electron yields of Au, Ag, Cu and Al derived with the new model are in good agreement with the results obtained from the scatters process simulation code-Casino.