The health condition of low-speed rolling bearing, such as the main bearing in wind turbines which bears the heavy dead weight and operates under variable speeds, has a big impact on the safe operation of the machinery. Therefore, damage detection of low-speed bearings plays a key role in the health management of large-scale rotating machinery. However, in popular vibration based bearing damage detection algorithms, due to the fact that the additional vibration features incurred by the low-speed operated bearing damage are typically weak in amplitude and low in frequency contents, the additional responses caused by damage are difficult to be isolated by conventional algorithms. Especially, in the cases of variable speed operations, the smearing effect caused by Fourier transform makes it more difficult to extract the damage features by spectrum analysis based methods. To deal with these issues, we developed a damage detection procedure specially designed for bearings operated at low and variable speeds. According to the dynamic properties of the vibration signals incurred by a low-speed bearing with damage, an envelope analysis method based on synchronous averaging with sliding narrow band-pass filters is designed and developed for extracting damage features in the low frequency range. The fundamental theory used in the method is derived first. Then, a damage detection signal processing procedure is constructed based on the elaborated theory. The feasibility and advantages of the proposed methodology are validated by numerical simulations as well as the measured data from a wind turbine field example.