A detailed study of the spectrum and variability of the source HESS J1745-290 in the Galactic Center (GC) region using new data from the H.E.S.S. array of Cherenkov telescopes is presented. Flaring activity and quasi periodic oscillations (QPO) of HESS J1745-290 are investigated. The image analysis is performed with a combination of a semi-analytical shower model and the statistical moment-based Hillas technique. The spectrum and lightcurves of HESS J1745-290 are derived with a likelihood method based on a spectral shape hypothesis. Rayleigh tests and Fourier analysis of the H.E.S.S. GC signal are used to study the periodicity of the source. With a three-fold increase in statistics compared to previous work, a deviation from a simple power law spectrum is detected for the first time. The measured energy spectrum over the three years 2004, 2005 and 2006 of data taking is compatible with both a power law spectrum with an exponential cut-off and a broken power law spectrum. The curvature of the energy spectrum is likely to be intrinsic to the photon source, as opposed to effects of interstellar absorption. The power law spectrum with an exponential cut-off is characterized by a photon index of 2.10 +/- 0.04_\mathrmstat +/- 0.10_\mathrmsyst and a cut-off energy at 15.7 +/- 3.4_\mathrmstat +/- 2.5_\mathrmsyst TeV. The broken power law spectrum exhibits spectral indices of 2.02 +/- 0.08_\mathrmstat +/- 0.10_\mathrmsyst and 2.63 +/- 0.14_\mathrmstat +/- 0.10_\mathrmsyst with a break energy at 2.57 +/- 0.19_\mathrmstat +/- 0.44_\mathrmsyst TeV. No significant flux variation is found. Increases in the gamma -ray flux of HESS J1745-290 by at least a factor of two would be required for a 3 sigma detection of a flare with time scales of an hour. Investigation of possible QPO activity at periods claimed to be detected in X-rays does not show any periodicities in the H.E.S.S. signal.