A hydrogen generating apparatus and a fuel cell power generation system having the hydrogen generating apparatus are disclosed. The hydrogen generating apparatus can include an electrolyte bath configured to contain an electrolyte solution, an anode placed inside the electrolyte bath and configured to generate electrons, a cathode placed inside the electrolyte bath and configured to receive the electrons from the anode to generate hydrogen, a condensation plate disposed on a transfer path of the hydrogen such that moisture carried in the hydrogen is condensed and the hydrogen is separated, and a heat exchanger configured to cool down the condensation plate heated by the moisture carried in the hydrogen. The hydrogen generating apparatus of the present invention can increase the efficiency of hydrogen generation by removing the moisture carried in the hydrogen while generating the hydrogen and reusing the moisture circulated through the electrolyte solution.