Neutrinoless double beta decay is a process that violates lepton number conservation. It is predicted to occur in extensions of the standard model of particle physics. This Letter reports the results from phase I of the Germanium Detector Array (GERDA) experiment at the Gran Sasso Laboratory (Italy) searching for neutrinoless double beta decay of the isotope Ge-76. Data considered in the present analysis have been collected between November 2011 and May 2013 with a total exposure of 21.6 kg yr. A blind analysis is performed. The background index is about 1 x 10(-2) counts/(keV kg yr) after pulse shape discrimination. No signal is observed and a lower limit is derived for the half-life of neutrinoless double beta decay of Ge-76, T-1/2(0 nu) > 2.1 x 10(25) yr (90% C.L.). The combination with the results from the previous experiments with Ge-76 yields T-1/2(0 nu) > 3.0 x 10(25) yr (90% C. L.).