In this letter, the self-powered solar-blind photodetector based on amorphous (a-) SnOx/crystalline (c-) Ga2O3 pn heterojunction with swift response speed has been successfully demonstrated. Increased hole concentration in a-SnOx by enhanced Sn2+ component under annealing improves the self-powered photoresponse performance. A highly precise test scheme without external supply captures the intrinsically swift response speed. The photodetector exhibits an impressive rise/decay time of 0.18/1.04 ms and responsivity of 7.08 A/W at 0 V bias, ranking into the top tier in all self-powered Ga2O3 photodetectors. This study provides a referenceable self-powered detector structure with amorphous/crystalline pn heterojunction.