The filamentous fungus Trichoderma reesei (teleomorph Hypocrea jecorina) is widely used as a cellulase producer in the industry. Herein, we describe the rational engineering of the publicly available T. reesei QM9414 strain to achieve a remarkable high-level production of cellulase on glucose. Overexpression of the key cellulase regulator XYR1 by the copper-repressible promoter Ptcu1 was first implemented to achieve a full cellulase production in the context of catabolite repression (CCR) while eliminating the requirement of inducing sugars for enzyme production. The T. reesei bgl1 gene was further overexpressed to compensate for its low β-glucosidase activity on glucose. This overexpression resulted in a 102% increase in FPase activity compared with the CCR-released RUT-C30 strain cultured on Avicel. Moreover, the saccharification efficiency toward pretreated corncob residues by crude enzymes from the engineered strain on glucose increased by 85% compared with that treated by enzymes from RUT-C30 cultivated on Avicel. The engineered T. reesei strain thus shows great potential as a viable alternative to deliver commercial cellulases after further optimization for efficient saccharification of agricultural waste.