The phtocount distributions of a quasi-thermal light source were measured by using the photoelectric counting method. The source was fabricated from the ground glass plate of 9${mu}{ extrm}{m}$ roughness illuminated by linearly polarized He-Ne laser beam. The coherence time of the quasi-thermal light changed from 31.4$mutextrm{s}$ to 2.48$mutextrm{s}$ according to the grain velocity of the ground glass plate. The photocount distribution showed the Bose-Einstein statistics for a long coherence time compared to the counting time interval, while the distribution approaches the Poisson distribution when the coherence time much shorter than the counting time.