Abstarct: There are many errors in PET (Positron Emission Tomography) that reduce image quality. One of these errors is the attenuation effect, which is best resolved by the PET/CT hybrid system. Another error is the gamma scattering error. This error occurs when one or both of the gamma rays in the body are scattered by Compton interaction. By putting an energy window for PET detectors, this error can be minimized. This increases not only the image contrast but also the sensitivity of PET. This study attempts to investigate the attenuation and scattering effect that are made by liver adjacent organs on PET imaging of liver tumor using Monte Carlo simulation method and optimize energy window in this imaging. For this purpose the Siemens PET BiographTM 6 scanner ring was simulated by MCNPX Monte Carlo code. Before examining the adjacent organs of the liver, a simple geometry of soft tissue and two kinds of 511keV gamma source –point source and spherical source (separately) - were simulated to investigate scattering effect of soft body tissue on PET imaging in chapter 3. Analysis of the results of simulation shows that, the majority scattered photons fall within the energy window (350-550 keV) without much loss of energy. The soft tissue, around the two sources at a distance of 8 cm from center, has the most scattering effect on PET imaging. In Chapter 4, PET imaging liver cancer was simulated by placing a complete human phantom with a tumor inside the liver (a 511 keV spherical gamma source) and inserting it in to the PET scanner ring. To examine each of the adjacent organs of the liver, that organ was removed from the complete Phantom of the human body, and then the counts of the PET detectors were compared in both complete phantom and phantom without that organ. The simulation result showed that the stomach and heart have the most destructive effect on image quality in imaging of the liver tumor and limiting the energy window to 435- 550 keV could be an appropriate way to remove these scattered photons. In order to gain more precision in results, the distribution of radiopharmaceuticals in body, in addition to the tumor, was also considered. Although the effect of adjacent liver organs on 511 keV gammas in this state is greater than in the previous case, the effect of the studied organs on the detector ring is still in the same range. In Chapter 5, bremsstrahlung radiation was investigated in PET imaging in soft tissue. To this end, one 511 keV gamma source inside a soft tissue sphere (to investigate the effect of secondary electron bremsstrahlung radiation) and the next a 18F positron source inside the same tissue (to investigate the effect of positron bremsstrahlung radiation) put inside the PET ring. Analysis of the simulation results showed that the Bremsstrahlung radiation resulting from the secondary electrons is of low energy, outside the energy window, and cannot influence PET imaging. The Bremsstrahlung radiation resulting from the positrons caused minor changes in the counts, and its negative effect on PET imaging can be reduced by making the energy window narrower from 350–550 keV to 417–550 keV. In Chapter 6, the effect of gamma scattering between PET ring detectors was investigated. To reach this goal, the all detectors of this ring were isolated. The analysis of the results of simulation shows that, although the isolation of detectors reduces this error, it can remove some true coincidences. Therefore, it does not have much effect on image quality of PET. Additionally, the problem of removing some true coincidences with a spherical soft tissue somewhat is resolved.