Flexible risers are used in the oil industry to transport liquids and gas from the seafloor to extraction and production equipment at the sea surface. Ongoing research aims at using composite materials instead of steel, in order to reduce weight and increase stiffness. Ensuring an optimal load transfer between the composite and metal components is very important. This paper presents an improved method for anchoring a flat fiber-reinforced tendon using a double grip system with self-locking grips. The novelty is the combination of new experimental results and finite element (FE) analysis to develop a superior dry friction grip. Experimental results are carried using a dedicated test setup, through which the test parameters can be accurately controlled. The efficiency of the grip system during pullout is superior to results obtained with flat grips. Numerical results offer an in-depth understanding of the influence between friction, geometrical parameters, and performance, making it possible to optimize the design. Results show that this grip system offers immediate technical applications, in a variety of conditions.