Cosmic ray muon-computed tomography (?CT) is a new imaging modality with unique characteristics that can be particularly important for applications in nuclear proliferation detection and international treaty verification. Using cosmic ray muons for nuclear security presents several potential advantages. Among others, muons are generated naturally in the atmosphere, can penetrate high-density materials, and are freely available. No radiological sources are required and consequently there is no associated radiological dose. Recently, the feasibility of using muons for imaging spent nuclear fuel stored in shielded casks has been explored and has been proved beneficial. However, challenges in ?CT imaging include low muon flux of ~10,000 muons/m2/min, the effects of multiple Coulomb scattering (MCS) blurring the image, and inefficiency in being able to use all recorded muons for imaging. In this paper, we argue that the use of muon tracing should produce tomographic muon images with improved quality – or more quickly for the same image quality – compared to the case where conventional methods are used. In our paper, we report on the development and assessment of a novel muon tracing method for ?CT. The proposed method back projects the muon’s scattering angle into each pixel crossed by its PoCA trajectory then forward projects the variance of the scattering angle in each pixel to detector bins along the muon’s incident horizontal direction. Two scenarios were simulated to assess the expected detection capability of this proposed method. GEANT4 was used to model the main characteristics of 1-60 GeV muons through matter. The simulated images showed an expected improvement in resolution and a reduced the reliance on the muon momentum information compared to a more conventional muon tomography method.