The kinked rebar configuration proposed by the authors has previously demonstrated improved seismic performance and progressive collapse resistance through quasi-static tests on reinforced concrete (RC) beams and plane RC frame substructures. In this paper, shaking table tests were conducted to evaluate the seismic performance of the novel RC frame structure with kinked rebar beams and post-yield hardening columns. The beams of the proposed frame included longitudinal bars with a kinked rebar configuration, while carbon fiber reinforced polymer (CFRP) bars were adopted in the columns to achieve post-yield hardening behavior. A 1/4-scale 4-story novel RC frame was designed, constructed, and tested, with three ground motion records of varying intensity levels used in the shaking table tests. The results showed that the inter-story and residual drift ratios of the proposed novel frame were effectively reduced compared to the conventional frame, indicating better seismic performance and self-centering capability. Additionally, the damage of the novel frame was first observed at beam ends and gradually became more severe with increasing seismic intensity. However, no obvious damage was observed at column ends, even under an extremely large earthquake. Thus, a “strong column-weak beam” failure mode of the novel RC frame structure was successfully achieved, and its repairability was effectively improved.