As one of the beam-to-column fully restrained connections that could shift the plastic hinges of the beam away from the face of the column, cover-plate reinforced connections are expected to be a practical choice for high strength steel frame seismic applications. Five cover-plate reinforced and one unreinforced welded flange-bolted web connection specimens combined with Q355 steel I-shaped beams and Q460 or Q690 steel box columns were designed according to Chinese codes and tested under cyclic loads at full scale. Failure modes, including local buckling of the beam, complete joint penetration (CJP) weld fracture, and column web fracture, were reported. The strength, stiffness, deformation, and energy dissipation features were analyzed. The four cover-plate connections met the AISC requirements for special moment frames (SMF) with maximum story drift angles greater than 0.06 rad and exhibited satisfactory seismic behavior. According to the test results, a limit on the ratio of the diaphragm plate to column plate thickness should be considered when the electroslag welding (ESW) process is used in high strength box columns. The strong panel zone designed with a panel zone resistance ratio (γpz) greater than 1.20 was recommended for box columns with steel strength no less than 690 MPa. Additionally, other design implications of the results were discussed.