The deep-ultraviolet (DUV) photodetectors (PDs) have many important applications in lots of fields; thus, developing self-powered DUV PDs and excavating the inherent mechanism seem seriously crucial for achieving further actual applications. The construction of heterojunction could lead to many desired characteristics in optoelectronic devices. In the field of DUV photodetection, Ga<sub>2</sub>O<sub>3</sub> has been a popular subject for constructing DUV PDs. So, it is necessary to develop self-powered Ga<sub>2</sub>O<sub>3</sub>-based DUV PDs via fabricating its heterogeneous structures. Therefore, in this paper, the Ga<sub>2</sub>O<sub>3</sub>/Al<sub>0.1</sub>Ga<sub>0.9</sub>N heterojunction DUV PD is fabricated and discussed, which could achieve 254 nm and 365 nm DUV light photodetection. At both positive and negative voltages, the heterojunction PD can operate with either a photoconductive mode or a depletion mode, respectively. In view of the PD performance, it displays decent dark current and DUV photoresponses. At voltage of 5 V and -5 V, under 254 nm DUV light illumination, the photoresponsivity (<i>R</i>) are 2.09 mA/W and 66.32 mA/W, respectively; while under 365 nm DUV light illumination, the <i>R</i> are 0.22 mA/W and 34.75 mA/W, respectively. In addition, driven by the built-in electric field (<i>E</i><sub>built-in</sub>), the <i>R</i> are 0.13 mA/W and 0.01 mA/W under 254 nm and 365 nm DUV light illumination, respectively. In all, the fabricated heterojunction PD displayed promising respects in the coming next-generation semiconductor photodetection technology. Results in this work indicate the potential of Ga<sub>2</sub>O<sub>3</sub>/Al<sub>0.1</sub>Ga<sub>0.9</sub>N heterojunction for performing high performance DUV photodetection. Furthermore, except for the characterizations of the materials and photodetector, in the end of this paper, the operating mechanism of the dual-band and dual-mode heterojunction PD is analyzed through its heterogeneous energy-band diagram. To conclude, the illustrated dual-band and dual-mode Ga<sub>2</sub>O<sub>3</sub>/Al<sub>0.1</sub>Ga<sub>0.9</sub>N heterojunction could be sensitive to UVA and UVC wavebands in the electromagnetic spectrum, that extends its photodetection region. And, the dual-mode (photoconductive mode and depletion mode) photodetection indicates two kinds of carrier transports in one PD, wihch could be attributed by the successful construction of the N-N tomo-type Ga<sub>2</sub>O<sub>3</sub>/Al<sub>0.1</sub>Ga<sub>0.9</sub>N heterojunction.