Abstract: Since X-ray CT dosage has been pushed to a low level and 3D imaging has been a trend, it is necessary to study the performance of 3D X-ray CT systems. In this work, we firstly propose a theoretical noise estimation method for 3D X-ray CT reconstructions. Then, we present four models for theoretical estimation of system performance for 3D X-ray CT based on FDK algorithm. The theories and analysis are based on Chaimellized Hotelling Observer (CHO). The Difference Of Gaussian (DOG) model is adapted for channels. The theories are validated by different numerical simulations. Our results demonstrate that theoretical estimation method of system performance for 3D X-ray CT accords well with the result from MC simulations. The proposed method for system performance evaluation can exempt us from some of computationally expensive Receiver Operating Character (ROC) studies. It can provide great convenience for system performance prediction and system design optimization. The method is easy to be extended to systems using other linear reconstruction algorithms.