Abstract: Direct X-ray imaging using a Fresnel zone plate (FZP) in the applications of laser plasma or inertial confinement fusion diagnostics has the potential for realizing high spatial resolution in the range of micrometers to sub-micrometers. For such an FZP imaging, the influences of the object size and the spectral bandwidth of the illuminating light have to be considered. In the simulations, numerical calculations such as the Fresnel-Kirchhhoff diffraction integral and convolutions have to be done, which will take a large amount of computer memories and cost a lot of computing time. In this paper we report improved algorithms for these numerical calculations by adopting the Monte-Carlo integration and a new algorithm of convolution. By simulating the two-dimensional imaging of an extended polychromatic X-ray source, it shows that the new algorithm has significant advantages in reducing the computing time over the past algorithms, and thus such simulations can be done by a desktop computer. The imaging indicates that with the increase of the object size and/or the spectral bandwidth, the image background is enhanced which causes the decrease of the contrast and also the image quality.