The deep-ultraviolet (DUV) photodetectors (PDs) have important applications in lots of fields. Thus, developing self-powered DUV PDs and excavating the inherent mechanism seem seriously crucial to achieving further actual applications. The construction of heterojunction can lead to many desired characteristics in optoelectronic devices. In the field of DUV photodetection, Ga₂O₃ has been a popular subject for constructing DUV PDs. So, it is necessary to develop self-powered Ga₂O₃-based DUV PDs through fabricating its heterogeneous structure. Therefore, in this work, the Ga₂O₃/Al_0.1Ga_0.9N heterojunction DUV PD is fabricated and discussed, which can achieve 254 and 365 nm DUV light photodetection. At positive voltages and negative voltages, the heterojunction PD can operate in 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 and –5 V, under 254 nm DUV light illumination, the photoresponsivity (R) is 2.09 and 66.32 mA/W, respectively, while under 365 nm DUV light illumination, R is 0.22 and 34.75 mA/W, respectively. In addition, under the built-in electric field (E_built-in), R is 0.13 and 0.01 mA/W for 254 nm and 365 nm DUV light illumination, respectively. In all, the fabricated heterojunction PD displays promising prospects in the coming next-generation semiconductor photodetection technology. The results in this work indicate the potential of Ga₂O₃/Al_0.1Ga_0.9N heterojunction with 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 dual-mode heterojunction PD is analyzed through its heterogeneous energy-band diagram. It is concluded that the illustrated dual-band dual-mode Ga₂O₃/Al_0.1Ga_0.9N heterojunction can be sensitive to UVA waveband and UVC waveband in the electromagnetic spectrum, extending its photodetection region. And, the dual-mode (photoconductive mode and depletion mode) photodetection indicates two kinds of carrier transports in one PD, which can be attributed to the successful construction of the N-N tomo-type Ga₂O₃/Al_0.1Ga_0.9N heterojunction.