M82 is a famous starburst galaxy which is dominated by young stellar populations and ISM. Some previous studies indicated the existence of intermediate-age and old stellar population in this galaxy, but little is known about them. We present a study of old globular clusters in M82 using the Hubble Space Telescope archive data. From the cluster survey of M82 we found 650 star clusters. We divided them into disk and halo star clusters according to their position. The color-color diagrams show that all 19 halo star clusters are old globular clusters. The disk sample may include both reddened young clusters and geniune old globular clusters. We estimated their ages using spectral energy distribution fit method with six filter data covering from ultraviolet (F330W) to infrared (F160W), and found that 30 of them are older than 3 Gyr. These are considered to be disk globular clusters. Twelve of the halo globular clusters are found to be partially resolved into their member stars. The (B-V) color range of the halo globular clusters is consistent with that of the Milky Way globular clusters, but most of M82 globular clusters are bluer than (B-V)=0.7. The existence of these old globular clusters suggests that the starburst galaxy M82 has an old stellar halo that may be as old as the Milky Way halo.