Based on the vector angular spectrum representation of the Maxwell equations and the method of stationary phase, only with the far field approximation, the analytical expressions of energy flux density of a hollow Gaussian beam diffracted by a circular phase aperture is presented. It is shown that the total energy flux of the beam can be expressed as the sum of the unapertured term and the additional term, where the additional term is the effect of the phase aperture on the beam; the total energy flux, the unapertured one and the additional one each can be expressed as the sum of TE term and TM term. The distributions of the total energy flux, the unapertuered one, the additional one, and their TE terms and TM terms are depicted in the far field. The influences of truncation parameter and the phase delay on the longitudinal total energy flux distributions are discussed.