An anchorage system for the tensile load transmission on the circular rods/tendons made from high-strength pultruded composites is proposed. The anchorage system comprises a composite rod having a spitted end with an inserted and glued metal wedge, a metal sleeve and pottant material, connecting composite rod and sleeve. The main objective of the system proposed is reduction of high stress concentration at the loaded end, which is typical for the bond-type anchor systems. The detailed analysis of 3D stress-strain state of the anchor was performed for pultruded CFRP/epoxy rod, steel sleeve, aluminum wedge and epoxy resin pottant. All calculations were made with finite element method accounting for elastic and elastic-plastic behavior of epoxy resin in shear. The principal conclusion resulting from these FEM calculations implies that stress concentration at the loaded end of the anchor system keeps independently of the wedge location if the adhesive bond between composite rod and pottant is available. The possible technical solution of this problem may be creation of a friction interface between composite rod and pottant within the anchorage length. To verify this suggestion, 3D contact FEM problems for the anchor system with the various lengths of friction interface were considered and analyzed. A series of the uniaxial tensile tests were carried out for the anchor systems made with CFRP pultruded rods of 5.5 mm diameter, steel sleeve of 300 mm length, A1 wedge of 110 mm length and cone angle of 7° embedded into epoxy resin. These experiments confirmed the working capacity of the anchor system proposed to transfer the tensile load on the high-strength UD CFRP/epoxy rod made by pultrusion. Failure of these CFRP rods was observed at the gauge section and maximum tensile stress of 2038 MPa. The anchor systems were fabricated with adhesive bond and only friction interaction between composite rod and pottant.