First results on a dark matter search done by the HEIDELBERG-MOSCOW double beta decay are resented. The experiment is running in the GRAN SASSO Underground Laboratory. A 2.9 kg ultra-low background HP-detector of enriched (86%) Ge-76, built to measure double beta decay, has been used to search for WIMPs. The measuring time is 60 days, corresponding to a statistical significance of 165 kg.d. Because of the extremely low background (0.067+/-0.002 counts.d.keV) in the region 10-100 keV we obtain improved limits for the heavy WIMP cross sections. Perspectives of the experiment are discussed.