Recent development in wireless communication technology and mobile equipment like PDA, cellular phone and GPS is making location-based services (LBSs) more popular day by day. However, because, in the LBSs, users continuously send queries to LBS servers by using their exact locations, private information could be in danger. Therefore, a mechanism for users' privacy protection is required for the safe and comfortable use of LBSs. For this, in this paper, we propose a grid-based cloaking area creation scheme in order to support continuous queries in LBSs. Our scheme creates a cloaking area rapidly by using grid-based cell expansion to efficiently support the continuous LBSs. In addition, to generate a cloaking area which lowers the exposure probability of a mobile user to a minimum level, our scheme computes a privacy protection degree by granting weights to the mobile users. Finally, we show from a performance analysis that our cloaking scheme outperforms the existing cloaking schemes in terms of response time and privacy protection degree.