P-type β-Ga2O3 films deep-ultraviolet (DUV) solar-blind metal-semiconductor-metal (MSM) photodetectors (PDs) are fabricated with extremely high photoresponsivity (9.5 × 103 A/W), external quantum efficiency (4.7 × 106%), detectivity (1.5 × 1015 Jones), and gain-bandwidth product (106) at 5 V bias, very low noise equivalent power (4.9 × 10−16 W/Hz1/2) and high specific detectivity (1.9 × 1013 Jones) at 1 kHz and 3 V bias. The excellent performances of the p-type β-Ga2O3 DUV MSM PDs are attributed to the charge carrier multiplication via collective excitation of aggregated excitons and/or electron-hole liquid within the fabricated high-quality p-type β-Ga2O3 films, which possess the room-temperature Hall resistivity of 52.6 Ωcm, the hole mobility of 41.4 cm2/V⋅s, and the hole concentration of 2.86 × 1015 cm−3. The unprecedentedly high photoresponsivity and detectivity and the carrier multiplication mechanism in high-quality p-type β-Ga2O3 films pave a novel way to fabricate super sensitive DUV PDs based on p-type wide-bandgap oxide semiconductors.