Geometric parameters that define the geometry of imaging systems are crucial for image reconstruction and image quality in x-ray computed tomography (CT). The problem of determining geometric parameters for an offset flat-panel cone beam CT (CBCT) system, a recently introduced modality with a large field of view, with the assumption of an unstable mechanism and geometric parameters that vary in each view, is considered. To accurately and rapidly find the geometric parameters for each projection view, we use the projection matrix method and design a dedicated phantom that is partially visible in all projection views. The phantom consists of balls distributed symmetrically in a cylinder to ensure the inclusion of the phantom in all views, and a large portion of the phantom is covered in the projection image. To efficiently use calibrated geometric information in the reconstruction process and get rid of approximation errors, instead of decomposing the projection matrix into actual geometric parameters that are manually corrected before being used in reconstruction, as in conventional methods, we directly use the projection matrix and its pseudo-inverse in projection and backprojection operations of reconstruction algorithms. The experiments illustrate the efficacy of the proposed method with a real offset flat-panel CBCT system in dental imaging.