A vertical diaphragm scheme is proposed to connect the concrete-filled thin-walled steel tube (thin-walled CFT) column and steel beam, as an alternative to horizontal diaphragm connections: dual vertical diaphragms are installed inside the steel tube, considering poor out-of-plane resistance of the thin tube wall. For verification of the moment connection, two experimental programs were carried out. In the first experiment, an ultimate tension test was conducted for flange-to-column connections, to identify the fundamental behavior of the proposed connection (i.e., strength, failure mode, and out-of-plane deformation). The design parameters, such as the thickness, number, and continuity of the vertical diaphragms, were considered. All the test specimens exceeded the design strengths based on a yield line model (i.e., the tensile capacity-to-demand ratios ranged Tu/TYL = 1.11–1.31), without early fracture of welded joints. In particular, at the design strengths, the tube out-of-plane deformations were more limited with the heavier diaphragms. In the second experiment, beam-to-column connections using prototype I-section steel were tested under cyclic flexure, to verify the joint flexural strength and rigidity as well as the seismic performance. The beam-to-column connections failed by the beam flexural mechanism, whereas damage was marginal at the joint wall (i.e., the flexural capacity-to-demand ratios ranged Mu/Mj = 0.87–1.09). Overall, the dual diaphragms were effective in achieving rigid (full-strength) connections with satisfactory plastic rotation of the beam. On the basis of the test results, design considerations were recommended for the vertical diaphragm connections.