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This paper proposes a new H ₂ output-feedback control with finite multiple measurement information for discrete-time systems with disturbances. This control is called an H ₂ finite multiple measurement output-feedback control (H2FMMOFC). The new control ascertains the H ₂ performance for disturbances and the equivalence to the H ₂ state-feedback control without disturbances on a finite measurement horizon. The boundedness and exponential stability of the proposed H2FMMOFC are also investigated. The gain matrices of the H2FMMOFC are obtained by solving a convex problem utilizing the linear matrix inequality tool. Via a numerical example, the H2FMMOFC is shown to ensure the H ₂ performance as well as the excellent robustness property against unexpected temporary model uncertainty although the uncertainty is not considered in its design.