In most safety applications within vehicle ad-hoc networks (VANETs), vehicles need to periodically broadcast messages with information of their precise positions to others. These broadcast messages, however, make it easy to track vehicles and will likely lead to violations of personal privacy. Unfortunately, most of the current location privacy enhancement methodologies in VANETs suffer some shortcomings and do not take driving safety into consideration. In this paper, we propose a safe distance based location privacy scheme called SafeAnon, which can significantly enhance location privacy as well as traffic safety. By simulating vehicular mobility in a cropped Manhattan map, we evaluate the performance of the proposed scheme under various conditions. The mean entropy, warning broadcast ratio, and mean silent period of SafeAnon scheme are increasing 58%, 281%, and 50% respectively than the random silent period (RSP) scheme. The total broadcast ratio is also 33% less than that in the RSP scheme.