Abstract: Based on the energy conversation law for a nonlinear evolution equation, blow-up of the initial value of its solution was investigated by using the improved convexity analysis method and the Sobolev s embedding theorem. A sufficient condition for blow-up of the initial solution of this equation was obtained, that is, the initial energyE(0)has a certain upper bound. And this upper bound is only related to the Sobolev s embedding constant in the discussed space.