An analytical expression for the diffraction of an elliptic Laguerre–Gaussian (LG) beam is derived and analyzed. We show that a beam with even singularity order has nonzero axial intensity for any degree of ellipticity and at any finite distance z from the initial plane, whereas at $z=0$ and $z=\infty$ the axial intensity is zero. We show that for a beam with a small degree of ellipticity and even order of singularity, two isolated intensity zeroes appear in the Fresnel zone on a straight line at an angle of $45\mathrm{deg}$ or $-45\mathrm{deg}$ , depending whether the beam’s spin is right or left. The theoretical conclusions are confirmed by numerical simulation and physical experiments.