In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process over an unreliable network. The stability of Kalman filtering with random packet losses is studied, where the packet losses are modeled by the Gilbert-Elliott channel model and the stability is measured by the so-called peak covariance stability introduced in [1]. We give two sufficient conditions for the peak covariance stability: one combined with a numerical method provides an accurate criterion, and the other is in a simple form and easy to check, both of which are shown to be less conservative than existing works in practice. Numerical examples demonstrate the effectiveness of our result compared with relevant literature.