Because of the importance of Gaussian beams in optics, particularly in the area of lasers, we devote the present paper to a study of the propagation of these beams. The Gaussian beam, also called a Gaussian spherical wave field, is basically a spherical wave field whose modulus in a plane transverse to the propagation direction varies in a Gaussian fashion. The fractional Fourier transforms (FRFT) were originally introduced in 1980 by Namias as a technique for solving theoretical physical problems. Since then lot of works have been done on its properties, optical implementations and applications; the fractional Fourier transform became an important tool in optics. It is of singular importance in the laser physics the study of the propagation and transformation of Gaussian beams. In this paper the fractional Fourier transform is applied to described the beam waist‐to‐waist transformation of Gaussian beams between input and output reference surfaces; for example, the waist‐to‐waist transformation of a Gaussian beam passing through a thin lens is necessary for beam focusing or modematching. Using the Collins formula and the fractional Fourier transform we can obtain the clear physical picture and simple calculation to study the propagation as well as the transformation of Gaussian beam, scaled variables and scaled field amplitudes are defined by complying with mathematical consistency; this relation provide a convenient way for analyzing and calculating the beam waist‐to‐waist transformation of Gaussian beams in the ABCD optical system.