By combining an existing concrete frame with a Y-shaped eccentrically steel brace， an innovative existing reinforced concrete-Y-shaped eccentrically steel brace structure with high lateral stiffness， good seismic performance and seismic resilience capacity was developed， and the existing concrete beam-shear link （ECB-SL） composite connection was a key point to achieve the expected seismic performance of the innovative structure. In this paper， specimens with endplate connection， U shape-side plate connection， U shape-angle connection and U shape-three side bolted connection， respectively， were studied by the cyclic loading tests， and the failure modes， hysteresis curves， skeleton curves， secant stiffness， energy dissipation capacity and load-strain curves were investigated. The test results show that the unexpected failure modes of specimens were anchor bolts tension or concrete cracking， so these composite connections cannot have enough bearing capacity. Specimen experienced a failure mode of link yielding， link buckling， concrete cracking， crack propagation， and link fracture. The failure mode， overstrength factor and inelastic rotation of the specimen were the same as those of the pure very short shear link， which was recommended in the design of ECB-SL composite connections.