High power microwave (HPM) source is attractive in generating gigawatt (GW) class microwaves based on the beam-wave interaction. Generally, HPM source with a high beam-wave conversion efficiency has a higher impedance. To improve the single-tube output power of HPM source, reducing the impedance of the device and increasing its power capacity are necessary. In this paper, a new low-impedance HPM source is proposed and proved to be capable of generating two phase-locked high power microwaves, which makes it promising to realize a higher combined power in a single HPM device.The new low-impedance HPM device consists of a two-cavity TKA (denoting the outer sub-source in the following) and a multiwave Cerenkov generator (referring to the inner sub-source below) inserted in the TKA inner conductor. These two sub-sources are connected in parallel and share a common magnetic field. A dual-concentric annular cathode is used in this microwave source, which is capable of emitting two concentric annular electron beams and driving the internal and external sub-source simultaneously. The advantages of this device are reducing the impedance and improving the injection electric power. When a voltage pulse is applied to the diode, part of microwaves generated in the inner subsource will leak into the outer sub-source (i.e., TKA) through the A-K gap. By amplifying the leakage microwaves, the TKA will be easily locked by the inner sub-source. Considering the fact that the microwave source consists of two sub-sources, the power capacity will also be greatly improved.As a result, particle-in-cell simulation indicates that when the diode voltage is 687 kV and the axial magnetic field is 0.8 T, two microwave beams that have a nearly identical frequency of 9.72 GHz and output powers of 1.20 GW and 2.58 GW respectively, are generated. The corresponding power conversion efficiencies are 28% and 30%, respectively. The frequency difference between these two microwaves fluctuates within 3 MHz and their phase difference is not in excess of 3. When the diode voltage changes from 665 kV to 709 kV, frequency difference between the two sub-sources fluctuates within 3 MHz and their phase difference fluctuation is within 5 in one voltage burst; the phase difference changes 10 in this voltage range. The impedance of this HPM source is as low as 36 .To sum up, the new HPM source proposed in this paper has a lower impedance and higher power capacity. The phase difference between the inner sub-source and the outer sub-source is very stable and favorable for the coherent power combination, which indicates that the new HPM source promises to realize a higher output power in a single-tube device.