An electron beam from a laser-plasma accelerator is converted into a gamma-ray source using bremsstrahlung radiation in a dense material. The gamma-ray beam has a pointlike source size because it is generated by a high quality electron beam with a small source size and a low divergence. Using this gamma-ray source, the radiography of complex and dense objects with submillimeter resolution is performed. It is the first evidence of a gamma-ray source size of a few hundreds micrometers produced with laser-driven accelerators. This size is consistent with results from Monte Carlo simulations.