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The needs and the feasibility of simultaneous computed tomography (CT) and magnetic resonance imaging (MRI) were recently reported. In this paper, a spiral magnetic resonance X-ray CT (MRX) imaging system is proposed for head and extremities imaging, which serves as a simple, cost-effective solution on the path to a full-scale CT-MRI fusion. While MRI and X-ray radiography were integrated before, we propose novel designs to acquire simultaneous CT and MR views for synchronized radiographic imaging or joint tomographic reconstruction. Our preliminary permanent magnet configurations achieve a magnetic field strength between 0.1 and 0.2 T while keeping weight low enough for portability. We have also shown that a field strength up to 0.35 T is achievable with permanent magnets that maintain a compact profile, though increased weight would hinder ease of transportation. Simulation results of a joint tomographic reconstruction scheme show the advantage of simultaneously acquired images. The proposed MRX system performs double helical scans in CT and MRI mechanisms, and has multiple niche applications, such as medical imaging on disaster sites, in battle fields, and for under-developed regions.