We investigated earthquake hazard parameters for Eastern part of Turkey by determining the a and b parameters in a Gutenberg-Richter magnitude-frequency relationship. For this purpose, study area is divided into seven different source zones based on their tectonic and seismotectonic regimes. The database used in this work was taken from different sources and catalogues such as TURKNET, International Seismological Centre (ISC), Incorporated Research Institutions for Seismology (IRIS) and The Scientific and Technological Research Council of Turkey (TUBITAK) for instrumental period. We calculated the a value, b value, which is the slope of the frequency-magnitude Gutenberg-Richter relationship, from the maximum likelihood method (ML). Also, we estimated the mean return periods, the most probable maximum magnitude in the time period of t-years and the probability for an earthquake occurrence for an earthquake magnitude >= M during a time span of t-years. We used Zmap software to calculate these parameters. The lowest b value was calculated in Region 1 covered Cobandede Fault Zone. We obtain the highest a value in Region 2 covered Kagizman Fault Zone. This conclusion is strongly supported from the probability value, which shows the largest value (87%) for an earthquake with magnitude greater than or equal to 6.0. The mean return period for such a magnitude is the lowest in this region (49-years). The most probable magnitude in the next 100 years was calculated and we determined the highest value around Cobandede Fault Zone. According to these parameters, Region 1 covered the Cobandede Fault Zone and is the most dangerous area around the Eastern part of Turkey.