The flux-weighted average cross sections and isomeric ratios of 92Mo(γ, n)91m,gMo and 92Mo(γ, 3n)89Mo reactions were measured through activation methods. Laser-driven bremsstrahlung γ-ray were generated by the laser wakefield accelerated quasi-monoenergetic electrons using the 200 TW laser in the Compact Laser Plasma Accelerator laboratory, Peking University. The results showed good agreements with previous works using traditional γ-ray sources, and were compared with TALYS 1.9 calculations. We extended the experimental results of 92Mo photonuclear reactions to higher energies, the experimental discrepancies of 92Mo(γ, n)91m,gMo isomeric ratios at high energy region were clarified, and the cross sections of 92Mo(γ, 3n)89Mo reaction were first obtained.