Positron emission tomography (PET) detects γ-ray emitted from the radioactive tracers injected in patient body via position sensitive detectors. The 3-dimensional (3D) activity distribution of the radiotracers can be obtained by image reconstruction of the raw data. On the other hand, computed tomography (CT) detects the attenuation coefficients of the patient body using x-ray. It provides relatively high-resolution image of the patient anatomy. Integrated PET/CT scanner provides medical, technical and economic merits as compared to standalone modalities. Researchers have been striving to improve the PET/CT technology over a decade, including detectors, image reconstruction algorithms and image analysis. All these endeavors aim for the better image quality and quantitation, with lower radiation dose. Attenuation correction using CT data is the most important correction in PET and is critical for improving image quality and quantitation. However, respiratory motion is generally considered to be one of the main factors which degrade the image quality in CT-based attenuation correction. This thesis aims to develop a new PET/CT attenuation correction method to reduce the respiratory motion misalignments between PET and CT and improve the PET quantitation. The first chapter of this thesis introduces the basic principle of PET/CT instrumentation, its role in detecting thoracic tumors, attenuation correction and respiratory misalignments in PET/CT. In the second chapter, several existing categories of the misalignment reduction methods are reviewed. The third chapter describes our proposed attenuation correction method, including theory, software and hardware implementation. The computer simulation and clinical study to evaluate our iv method are discussed in chapter 4 and 5 respectively. The conclusion and future work are demonstrated in the end of this thesis.