Mobile-aware service systems are dramatically increasing the amount of personal data released to service providers as well as to third parties. Data may reveal individuals' physical conditions, habits, and sensitive information. It raises serious privacy concerns. Current approaches to mitigate the privacy concerns rely on the randomization. However, it is difficult to guarantee privacy levels with random noise. In this paper, we propose a data obfuscation mechanism based on the generalized version of the notion of differential privacy. We extend the standard definition to the settings where the inputs belong to an arbitrary domain of secrets. Then we enhance the mobility signature privacy with our mechanism. By adopting the expected distance as an indicator to measure the service quality loss, we compare our mechanism with the (k,d)- anonymity random method. On the real dataset, the results reveal that our mechanism adds less noise under the same privacy guarantee.