Computed tomography of chemiluminescence (CTC) is one kind of volumetric tomography which can recover 3D flame structures and has found extensive applications for spatiotemporally resolved measurements of flames. However, the existing CTC techniques rely on the pinhole model and fail when the flames are confined within a cylindrical glass due to image distortion caused by the refraction on both the internal and external surfaces of the glass. In this work, a refined camera model was developed by combining the pinhole camera model with Snell's laws using a reverse ray-tracing method to incorporate the effects of refraction. A proof-of-concept demonstration of CTC based on the refined camera model was conducted on a swirl flame confined within a 20-mm-thick K9 glass. The results proved the superiority of such technique against the existing version in terms of reconstruction accuracy. This work is expected to be especially useful for the study of combustion phenomena such as combustion instability for which the flames are typically confined within cylindrical combustors.