In this study, a modified Mach-Zehnder (MZ) interferometer is used to measure the orbital angular momentum (OAM) [the value and sign of topological charge (TC)] of a Laguerre-Gaussian (LG) beam. Simulated results are found to be consistent with the experimental results. Vortex-like petal patterns are observed when the LG beam interferes with the Gaussian beam. The number of petals is found to be equal to the absolute TC value of the LG beam, and the rotational direction of the interference patterns is related to the TC sign: at a positive TC value, the interference patterns show a clockwise rotation, whereas at a negative TC value, the interference patterns show a counterclockwise rotation. The OAM state can be accurately determined based on the interference patterns only when the spot size of the LG beam is smaller than that of the Gaussian beam. When the spot size of the LG beam is close to that of the Gaussian beam, the interference patterns reflect only the TC value and the TC sign cannot be identified. Compared with the conventional interferometers, the proposed interferometer can obtain a stable interference pattern and directly obtain the OAM state of the LG beam. The experimental phenomenon is obvious. The findings of this study provide a reference for the theoretical analysis of the interference between the LG and Gaussian beams and establish a research foundation for the spin-orbit interaction between light and matter.