An electron beam is obtained using laser wakefield electron accelerator, and converted into a \gamma-ray source after undergoing bremsstrahlung radiation in a dense material. A quasi-monoenergetic structure is observed when the length of the plasma channel was modified. The structure has a 58-MeV peak energy, 15-mrad (full-width at half-maximum) divergence angle, and 340-pC charge. The \gamma-ray source generated by this high-quality electron beam is brighter and has higher spatial and temporal resolutions than other conventional sources. A \gamma-ray radiography demonstrational experiment is performed. Pictures of a ball with different layers made of different materials are taken. The results show a clear structure and density resolution.