The letter provides alternatively a simple way of computing the Fresnel field integral, a further extension to the Gaussian-beam expansion. The zeroth-order Bessel function of the first kind is expanded into an approximate sum of Gaussian functions. The field integral is then expressible in terms of these simple 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.