It has become a common practice to create circular or rectangular openings in beam webs to provide space for pipes, ducts, and so on in modern steel construction. The post-earthquake study has shown that such reduced web section (RWS) connections can effectively remove plastic hinges from column faces, improving the connection ductility. However, more experimental work is still needed on RWS connections with circular openings. This paper presents the results of cyclic testing on 1/3 SN400YB steel H-beam-to-H-column connections with improved bolted web and welded flange (BWWF) details and circular openings. In detail, the center of the circle was located away from the column face with a distance equal to 0.9 beam depth. The ratio of diameter to beam depth increased to over 0.7. The connections were tested under a column loss scenario. The AISC 341 protocol was used in comparison with a near-fault one with a large displacement pulse varying from −2% to +6% drift. The results indicate that the connection can meet the AISC seismic requirement if the circular opening has a diameter smaller than 0.65 beam depth. The results also show that a crack may initiate from the heated affected zone of a circular opening created by thermal cutting after the connection is exposed to a large displacement pulse. All that implies a need to study further the effects of thermal cutting and a large displacement pulse on RWS connections with circular openings.