The blowup phenomena of the solutions for the initial-boundary value problem of the non-isentropic Euler equations with damping is studied. It is proved that the solutions will blow up in finite time when a weighed functional associated with the initial momentum is large enough by using the integration method. Some recently known blow-up results are extended from the isentropic case to the non-isentropic case. And the blow-up result for the negative initial entropy case is obtained without the restriction that the adiabatic constant is not bigger than three.