One of the main concerns related to flat reinforced-concrete (RC) slabs is the slab's punching capacity. Punching can occur not only due to a deficient transverse reinforcement, but also when the flexural capacity of the slab needs to be increased. To increase the flexural capacity, carbon-fiber-reinforced-polymer (CFRP) composites have been applied according to near-surface-mounted (NSM) or external-bonded-reinforcement (EBR) techniques, while for the punching strengthening CFRP reinforcements have been applied according to embedded-through-section (ETS) technique. To take advantage of strengthening benefits of the NSM and ETS techniques, in the present paper a new type of CFRP laminate of U-shape is used by adopting a novel hybrid technique for the simultaneous flexural and punching strengthening of existing RC slabs. Besides, this hybrid technique aims to provide a better bond performance for the ETS and NSM CFRPs by improving the anchorage conditions. Moreover, a higher resistance to the susceptibility of occurrence of other premature failure modes, like concrete cover delamination, is offered by using this hybrid technique. A 3D nonlinear finite-element (FE) model is developed to simulate the experimental tests by considering the nonlinear behavior of the constituent materials. The experimental program and numerical model are described, and the relevant results are analyzed.