We study the population of compact stellar clusters (CSCs) in M81, using the HST/ACS images in the filters F435W, F606W and F814W covering, for the first time, the entire optical extent of the galaxy. Our sample contains 435 clusters of FWHM less than 10 ACS pixels (9 pc). The sample shows the presence of two cluster populations, a blue group of 263 objects brighter than B=22 mag, and a red group of 172 objects, brighter than B=24 mag. Based on the analysis of colour magnitude diagrams and making use of simple stellar population models, we find the blue clusters are younger than 300 Myr with some clusters as young as few Myr, and the red clusters are as old as globular clusters. The luminosity function of the blue group follows a power-law distribution with an index of 2.0, typical value for young CSCs in other galaxies. The power-law shows unmistakable signs of truncation at I=18.0 mag (M_I=-9.8 mag), which would correspond to a mass-limit of 4x10^4 M_solar if the brightest clusters are younger than 10 Myr. The red clusters have photometric masses between 10^5 to 2x10^7 M_solar for the adopted age of 5 Gyr and their luminosity function resembles very much the globular cluster luminosity function in the Milky Way. The brightest GC in M81 has M_B^0=-10.3 mag, which is ~0.9 mag brighter than w-Cen, the most massive GC in the Milky Way.
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