According to Lamb′s semiclassical laser theory, whether the two modes in a solid-state laser can oscillate simultaneously depends on the mode-coupling coefficient between them. The coupling coefficient is defined as the ratio of cross-saturation factors and self-saturation factors. A dual-frequency Nd∶YAG solid-state laser is built with two quarter-wave plates, and the frequency difference from 30 MHz to 1.3 GHz is obtained. On this basis, the noise power spectrum density of two orthogonally polarized modes is measured under different frequency differences, by which the coupling coefficients of gain competition between two modes are calculated. In theory, based on the Lamb′s semiclassical laser theory, the coupling coefficient expression is deduced, and the trend that the coupling coefficient decreases with the increasing of frequency difference is verified. The factors influencing the coupling coefficient are analyzed. It provides the theoretical foundation for further optimization of dual-frequency solid-state laser.