With the development of field emission x-ray cold cathodes of nanomaterials, several new x-ray imaging geometries have been proposed. Compared with thermionic x-ray tube, this new type of x-ray tube is of great advantages, such as fast response, low energy consumption and individually addressable switching. In this work, a new tomographic geometry is devised, in which a stationary polygon-shape flat-panel cathode source array is employed to avoid mechanical movement for scanning. With an array of sources implemented in a flat-panel, each source irradiates a narrow cone beam x-ray and all the beams from the panel are overlapped to cover the scanned object. A number of the flat-panels, as well as x-ray detectors of the same number, are grouped as a polygon that encloses the object to implement a rotation-free projection acquisition. With the proposed geometry, we experimentally explore two scanning schemes, i.e., switching source separately or simultaneously. Numerical experiments demonstrated that in separating switching, low root mean square error and high contrast to noise ratio is achieved with more sources distributed in the flat-panel. For simultaneous switching, image quality is restricted by few-view nature and overlapping projection. With the limitation of constant current power and x-ray dose, the scheme of 10×10 sources distributed in the flat-panel can produce an advisable reconstruction result.