Protecting the location privacy of source and sink nodes in a sensor network is an important problem. Source-location privacy is to prevent event source tracking by adversaries and sink-location privacy is to protect sink nodes from adversaries who try to disrupt the sensor network. In this paper, we propose a constant-rate broadcast scheme for ensuring their location privacy. This scheme (1) equalizes traffic patterns of the sensor network to deal with eavesdropping and (2) minimizes the routing information of each sensor node to deal with node compromising.We further reduce the overhead of the proposed scheme by proposing a forwarder-driven broadcast (FdB) scheme that allows efficient multiple broadcasts with smaller buffer usage. Analysis and evaluation results show that FdB can support multiple broadcasts with small message delivery time and buffer usage.