Laser accelerated high-energy electron beam has the properties of small source size, quasi-monoenergetic, and short duration. In this paper the radiography by the electron beam is simulated using a Monte-Carlo code. Various radiographies are simulated, such as a step target and a thick iron block of inside cracks by a collimated 200-MeV beam, a modelled inertial-confinement-fusion target by a 11-MeV point-like beam, and the deflectometry of a 70-MeV electron beam by a laser plasma generated magnetic field. The obtained results indicate that the radiography by a laser-accelerated electron beam is of high spatial resolution and sensitivity in the detection of the inside defects of material, identification of the interface of thin material, and diagnosis of electromagnetic field.