A new conceptual design of muon catalyzed hybrid deuterium-deuterium fusion reactor is presented and its energy production and gain for different ion densities are determined. It is shown that the energy gain of 6.59 is achievable with the suggested system for deuterium of liquid hydrogen density. Its comparison with a similar deuterium-tritium hybrid fusion reactor has shown that at lower densities of LHD - 10 LHD the similar gain of 6.59-6.86 is achievable. For a deuterium density of 100 LHD, the obtained gain is 7.16, which is 10 times more than the gain of a muon catalyzed d+d reactor. The calculated gain was at temperature <0.01 eV, and for this reason the obtained gain was small in comparison with a similar muon catalyzed d+t hybrid system. Finally, the availability of deuterium, an absence of radio-activity, tritium handling and inventory problems and the simplicity in using this suggested system as a central component for the satellite purposes of a nuclear power station all suggest that the proposed system has good potential.