In this paper the fan beam reconstruction model （convolution-back projection） and its computation formulae are firstly reviewed. But the speed of computation is rather low

because these formulae are so complex that the quantity of computation is too large. In order to increase the speed of computation a fast algorithm has been developed. Under the same subjective and objective image fidelity the computational speed of the new algorithm has been increased by a factor of two in comparison with that of the conventional algorithm. This algorithm has been used in the reconstruction of some simple practical models. The result of the computation shows that this algorithm can be easily realized by hardware

because only one function （SIN） is used rather than many functions （TAN

ARCTAN and SQR etc.） involved. The algorithm can also be used in the x-ray computerized-tomography system and acoustic non-destructive detectors.