The invention discloses a shear-type eccentric support energy-dissipating beam and a shear-type eccentric support structure, and belongs to the technical field of steel frame support structures. The shear-type eccentric support energy-dissipating beam comprises an upper flange, a lower flange, a web and first stiffeners. The upper flange is parallel to the lower flange. The web is perpendicular tothe first stiffeners. The web and the first stiffeners are connected with the bottom of the upper flange and the top of the lower flange at the same time, wherein the web is provided with through holes that at most run to the bottom of the upper flange or the top of the lower flange. The shear-type eccentric support energy-dissipating beam and the shear-type eccentric support structure have the advantages that the through holes not running through the height of the web help decrease the height of the web to effectively bear shear action, and steel consumption of the overall eccentric supportstructure is reduced; the reduction in the steel consumption for the eccentric support structure is not limited to the limits, upon web height and thickness, in the existing technical specifications;therefore, the beam allows the steel consumption of the eccentric support structure to be far lower than that of related arts, and engineering construction cost is further reduced.