This paper proposes a novel entropy-based metric for evaluating silent cascade which is a prevalent trajectory privacy preserving method in LBSs (location-based services). Within this measure, the trajectory privacy is quantified as the probability of the relevance between the user’s pseudonym before and after each mix-zone. After a period of time, the tracked user may take many potential trajectories from the perspective of the adversary. The user’s trajectory privacy level is calculated using information entropy. The most distinguishable aspect of the measure is to take into account the adversarial background knowledge. We develop methods to describe and quantify the adversarial background knowledge. Simulation results reflect the impact of background knowledge on the privacy level in the metric, and show that this metric is effective and valuable to measure the user’s trajectory privacy level correctly even the adversary has variable background knowledge.