An x-ray shadow projection microscope using a scannable point source of x-rays is under development at SUNY. The point source is generated by a focused electron beam that can be steered electromagnetically in a plane perpendicular to the optical axis of the microscope. The specimen is mounted on a rotatable mechanical stage for microtomography. An elaborate feedback system is being implemented to measure and correct the motion error of the mechanical stage. The conventional cone-beam image reconstruction algorithm suffers from two constraints. Firstly, the specimen must be contained in a sphere-like reconstruction region. Secondly, the x-ray source must be moved along a circle in the specimen coordinate system. Considering the characteristics of the x-ray microscope system of ARTS-AMIL and the limitations of the conventional cone-beam reconstruction algorithm, a general cone-beam image reconstruction algorithm is presented. The general algorithm can be applied to various scanning geometries, such as polygonal, helical, or random scanning patterns, for different reasons. In order to study the general cone-beam reconstruction algorithm, a computer simulation has been performed. With various scanning parameters, projection data were generated mathematically and then the general cone-beam reconstruction algorithm tested with the simulated data. The experimental results shows that the different kinds of scanning loci of the x-ray source consistently resulted in satisfactory 3-D reconstructed images.