We provide alteatively a simple way of computing the Fresnel field integral,a further extension to the Gaussianbeam expansion.With a known result that the circ function is approximately decomposed into a sum of Gaussian functions,the zero-order Bessel function of the first kind is similarly expanded by the Bessel-Fourior transform.Two expansions are together inserted in this integral,which is then expressible in terms of the simple algebraic functions.The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics.As examples,the calculation results for the uniform and the simply supported piston sources are presented,in a good agreement with those evaluated by numerical integration.