A multiregion integral kinetic (MIK) code based on the integral kinetic model and a Monte Carlo neutron transport method has been developed with a new time-dependent feedback modeling capability. The current MIK code is applicable to the supercritical power transient following reactivity insertion in a fissile system of arbitrary geometry and composition, taking its feedback mechanisms into account. The new time-dependent feedback modeling capability allows a more direct and accurate treatment of complicated and nonlinear feedback mechanisms in a given system. The purpose of this study is to verify the MIK code and its time-dependent feedback modeling capability through various supercritical transient experiments conducted at the Godiva, TRACY, and SILENE facilities. Specifically, four supercritical experiments were selected and simulated using the MIK code. The various complicated feedback mechanisms—thermal expansion in Godiva, and Doppler broadening, thermal expansion, and radiolytic gas creation in TRACY and SILENE—provide a good benchmark for verifying the MIK code and its time-dependent feedback model. The obtained results show generally good, albeit occasionally poor, agreement with experimental results depending on the specific experiment. When the reasons for the poor agreement are considered, however, it may be concluded that the simulated results show promising agreement with the experiments, verifying the MIK code and its time-dependent feedback modeling capability.