Abstract: In fan-beam computed tomography, the source-to-origin distance sometimes varies. In this case, some reconstruction formulae were educed which included the derivative of the source-to-origin distance with respect to the rotation angle, and this feature was not favorable for the practical application. A derivative-free noncircular fan-beam reconstruction formula was brought forward by Ge Wang,,Tein-Hsiang Lin and Ping-chin Cheng. And they proved that the formula was accurate under the condition that the three assumptions were satisfied. But in the course of the deduction, there exists some errors. This paper has pointed out the errors, and made some discusses on the result. Computer simulations give some good results.