The paper deals with the level-crossing intervals of a stationary random process. Probability densities of the level-crossing intervals of a process consisting of a sine wave plus Gaussian random noise are experimentally investigated by digital simulation. The Gaussian random noise is selected to be of 7-th order Butterworth power spectrum density. The obtained probability densities appear with a number of isolated peaks much larger than the number observed on the corresponding probability densities of the Gaussian noise alone. When the sine wave frequency is greater than or approximately equal to the half of the cutoff frequency of the noise spectrum, experimental data suggest that each isolated peak has a Gaussian-like density. The mean time interval associated with each Gaussian-like density is equal to a multiple number of the period of the sine wave, while the variance is found to be fairly the same for all peaks of a same probability density. The assumption of "quasi-independence" is not valid for the level-crossing intervals of the present process.