This research proposes connection configurations of two types for non-intersecting H-section steel beam and column. To elucidate the mechanical behavior of the proposed connections, full-scale moment connection tests and finite element analyses were conducted using T-shaped partial frame models. Comparisons between the proposed connections and regular intersecting connections demonstrate that the proposed connection is able to provide sufficient stiffness and energy-dissipation capacity if the beam and column flanges are designed to provide sufficient shear resistance. Then to understand the global behavior of frames using the proposed connections, pushover analyses of a two-story two-span frame were conducted. Because the bending moment of the beam acts on the column by a torque through the proposed connections, torsion spring models were incorporated for representing the proposed connections in 3D frame analysis. Analysis results showed that the girders and columns exhibited lower stiffness and strength than those of frames with intersecting connections because of torsion. To overcome this issue, torsion restraint by secondary beams with different configurations was discussed and optimal configuration was suggested. By utilizing the optimal configuration, torsion of girders and columns can be efficiently reduced into a similar level as that of regular intersecting connections.