Vehicular ad hoc network (VANET) is an emerging new communication technology which has attracted a lot of research attention from academic community and industry. It is promising technology to provide safer and efficient traffic conditions. This is realized by letting vehicles to exchange safety messages. This messaging increases the awareness of vehicles about their neighboring vehicles positions and warns drivers about dangerous situations. However, availability of such information facilitates the tracking of vehicles. So, this information must be protected against the potential misuse. In this thesis, we address the problem of achieving location privacy in VANETs with randomly changing identifiers (i.e. pseudonyms) in the presence of a global passive adversary. We suggest adding a random delay to message broadcast period after the vehicle update its pseudonym in mix zones. By this way, we want to mitigate the linkability between pseudonyms. This could help to make tracking more difficult and increase safety and confidence of drivers using VANET. Instead of adding delay to safety messages completely random, one step taken further and delay is added according to the silent vehicle number in mix zone. We also investigated the effects of different number of mix-zone placements in the network to the location privacy of users. Several simulations have been performed to evaluate the performance of the systems. The results of experiments show that adding delay to message broadcast period improves location privacy of drivers in VANET and also provide information about the relationship between the strength of the adversary and the level of privacy achieved by changing pseudonyms.