Steel reinforced polymer (SRP) composite has recently emerged as an effective and economical solution for strengthening of reinforced concrete (RC) structures. Premature debonding failure of unanchored SRP at low load levels generally governs the performance of RC structures strengthened with externally bonded SRP. Therefore, a novel yet simple spike-shaped anchorage system was proposed in this study to prevent the debonding failure of SRP and to improve the interfacial shear capacity. Experimental investigation through single-lap shear tests of SRP-concrete joints showed that the anchorage system changed the failure mode from composite debonding to fiber rupture. In addition, the anchorage system substantially increased the peak load and reduced the interfacial slippage of the SRP-concrete joint compared to the unanchored condition. A numerical procedure based on the finite difference method was developed to predict the full-range load response, and results matched well with the full-range experimental responses of anchored and unanchored specimens. Parametric study of the test results and numerical simulation based on finite difference method both showed that the fiber rupture failure mode could be achieved for anchors in various positions along the bonded length. The closer the anchor is to the loaded end, the less global slip was obtained when the load reached the peak value.