A multi-stage traveling-wave waveguide-based spatial power divider/combiner using waveguide-to-microstrip (Wg-Ms) probe-pair coupling structure is proposed and applied to the design of a broadband power-combined amplifier module at Ka-band. An eight-way passive back-to-back power divider-combiner with four-stage Wg-Ms probe-pair transitions has been designed, fabricated, and tested. The measured overall insertion loss is less than 1.5 dB from 28 to 40 GHz, which demonstrates the low-loss performance of the proposed multi-way dividing/combining structure. Based on the passive power divider/combiner, an eight-device power-combined amplifier has been implemented with eight broadband medium power amplifier chips. The measured small-signal gain of the amplifier is more than 18 dB and the output power at 1-dB gain compression (P-1 dB) is higher than 30 dBm in the frequency band of 28–40 GHz. Power combining efficiency is within the range of 76–88%. Furthermore, the performance degradation of the power-combined amplifier due to device failure is also analyzed and tested. The experimental result indicates the reliability of this type of power-combined amplifier.