Abstract: The far-field irradiance distribution of a Gaussian beam which is transmitted from telescope with certain center obscure is researched in this paper. First, We derive a representation of irradiance distribution in far field of a Gaussian beam through a obscured telescope without beam's random jitter, and then give a approximation formula of encircled power and spot radius of certain encircled power ratio with and without beam's jitter due to telescope's center obscure. Finally, We researched the joint effects of truncation and obscure on a Gaussian beam's far-field energy distribution.