For proper attenuation correction of SPECT images, a set of 3D attenuation maps specific to the imaging slices is needed. Among the many different approaches for deriving the attenuation maps, fan beam transmission CT (FBTCT), performed on the same SPECT system as emission imaging, has many promising and clinically practical features. The major problem of FBTCT is that the current SPECT systems do not have a large enough field of view (FOV) to cover the typical cross-sectional size of patients. To address this problem, we have developed a novel asymmetric fan (AsF) sampling scheme to extend the FOV to practical sizes for clinical TCT imaging on existing SPECT systems. This AsF scheme samples only half of the intended FOV in each projection; the other half would be sampled in an opposing projection after detector rotation. We have implemented the AsF sampling on a three-head SPECT system through a specially designed source-collimator assembly. We have modified the conventional convolution backprojection algorithm to facilitate simple and fast image reconstruction. The feasibility of the approach is confirmed by the quality of the derived TCT images of various phantoms and human subjects. The AsF sampling scheme could also have applications in other general transmission CT systems.