In this study, the cracks growth rate in the 13th row of the T56 compressor blades was studied to investigate their fatigue life. For this purpose, the centrifugal and aerodynamic forces on the blade were calculated and then the resulting stress field was obtained by using finite element method. Then, the critical points of stress were determined and the initial semi-elliptical cracks were modeled at these points. After modeling of the initial crack, the stress intensity factor on the crack front was calculated by ANSYS software. Furthermore, the number of required cycles for the crack growth and blade fracture were calculated by applying Paris law to a certain value. After crack growth at this stage, a crack with new length was also modeled at the same point and all the mentioned stages for its growth, were repeated. In this paper, the modal analysis of the blade was conducted and normal frequencies with possible stimulation on compressor velocity were determined by Campbell Diagram. After determining the stress field at resonant frequency, all stages of crack growth were repeated under these conditions to calculate the fatigue life.