The privacy of a person leveraging a navigation service may be compromised due to the threats involved in sharing location information. However, at the same time, sharing location information is essential for taking advantage of location-based services. In this talk we present a novel Mixed Integer Linear Programming based framework that, given the navigation requirement of a user with the requirement of staying at some private locations for some time, synthesizes an optimal trajectory satisfying the navigation requirement of the user, along with another trajectory that satisfies the privacy requirement of the user while ensuring the maximum overlap with the optimal navigation trajectory. While the first trajectory is used for navigation, the second trajectory is used to transmit the locations of the user to the location-based service providers to exploit location-based service as much as possible without compromising the privacy of the user. We implement our algorithm to develop an Android application and create a modified version of Android OS for such privacy-preserving navigation and evaluate its efficacy through thorough experimentation on several city maps. Experimental results establish that our approach has the potential to pave the way for mobile users to utilize location-based services without being concerned about their location privacy.