Direct X-ray imaging by a Fresnel zone plate (FZP) has achieved a spatial resolution of 10 nm on a synchrotron beamline. It may be used to obtain submicron-resolution X-ray images of laser-plasma sources or fusion targets. However, none of previous imaging experiments with laser-plasma kilo-elelctron-volt X-ray sources shows such a high resolution. In comparison with the FZP imaging on a synchrotron, we consider a case of imaging an extended object with a laser-plasma X-ray source that the illumination monochromaticity is lower and the field of view larger. Our simulations show that the spatial resolution is affected by both the object size and the spectral bandwidth of the source, which can explain the previous experiments. We conclude that by using a 100-zone FZP to image an object with up to 700 μm in size, a spatial resolution better than 1 μm can be realized by using X-rays of several kilo-electron volts and a spectral bandwidth just less than 3%. In this paper, we report a proof-of-principle study in simulation and experiment in an optical range centered at 632.8 nm. The simulation is performed with the same method as that previously used for X-ray imaging but with a 100-zone FZP working in the optical range. Simulations show that with the increase of the object size, the field-of-view contrast is degraded, but the spatial resolution is nearly unchanged. With the increase of the spectral bandwidth for the illumination, both the contrast and the resolution are degraded. In the experiments, different spectral bandwidths are realized by band-pass filters and different object sizes by an adjustable aperture. The experimental results are confirmed to be in agreement with the simulations. These results reveal that given a satisfied spectral bandwidth of laser-plasma X rays, the FZP imaging will be a promising approach to 1 μm or higher resolution X-ray imaging of a 1-mm-size object.