An innovative self-centring precast steel-concrete hybrid (SPH) frame was proposed. The proposed SPH frame was assembled with reinforced concrete (RC) columns and prefabricated steel-concrete hybrid (PH) beams using steel end plates and high-strength bolts. The RC columns consisted of a traditional RC section and an unbonded post-tensioned (PT) screw-thread steel (STS) bar, and the PH beam was composed of two steel beam ends, a prefabricated RC beam unit and four unbonded PT strands. The self-centring ability of the structure system was mainly provided by the PT steel reinforcements; the energy dissipation capacity was mainly provided by the bolted web friction devices (WFDs) applied to the beam and the plastic deformation of the steel beam ends. To examine the seismic behaviour of this innovative structural system, cyclic tests were conducted on two SPH frames and one non-prestressed precast steel-concrete hybrid (NPH) frame. By analysing failure modes, hysteretic loops, skeleton curves, energy dissipation, displacement ductility ratios, stiffness degradation and the relative self-centring efficiency (RSE), the effects of the initial prestress, the pretorque of the high-strength bolts at the WFDs and the construction measure at the column base were thoroughly assessed. The test results indicated that the proposed noncontact oil jack prestressing technique used in the PH beams was reliable; during the testing process, gap opening and closing could be clearly observed at the interfaces between the RC beam unit and the steel beam end; the SPH frames exhibited better self-centring and energy consumption capabilities than the NPH frame; and the SPH frame exhibited a typical two-stage cyclic behaviour, namely, a self-centring stage and an energy consumption stage. In the self-centring stage (before the drift ratio of 2.0%), the SPH frame could effectively control residual deformation, and the RSE remained at approximately 85%; in the energy consumption stage (after the drift ratio of 2.0%), the SPH frame could effectively consume the absorbed energy. Based on the test results, a moment calculation method, which could distinguish the gap opening in the PH beam, was proposed, and the calculated results agreed well with the experimental results.