This paper presents a new approach to predict chatter stability in cutting considering process damping. Traditional chatter stability analysis methods enable to predict stable or unstable conditions. Under unstable conditions, the chatter vibration can increase theoretically infinitely. However, chatter vibration is damped at a certain amplitude in real process due to process damping, i.e., the cutting process is stabilized by means of tool flank face contact to the machined surface. In order to consider the influence of the process damping, a simple process damping force model is introduced. The process damping force is assumed to be proportional to the structural displacement. The process damping coefficient is a function of the vibration amplitude and the wavelength. In order to identify the coefficients, a series of finite element analysis is conducted in the present study. Identified coefficients are introduced into the conventional zero-order-solution in frequency domain. The proposed model calculates chatter stability limit assuming process damping with finite amplitude. Hence, this analysis enables to estimate the amplitude-dependent quasi-stable conditions. Analytical results for thee face turning operation demonstrated influence of process damping effect on resultant vibration amplitude quantitatively.