Range-free localization approaches are cost-effective for mobile sensor networks (because no additional hardware support is required). However, existing range-free localization approaches for mobile sensor networks suffer from either sparse anchor node problem or high communication cost. Due to economic considerations, mobile sensor networks typically have sparse anchor nodes which makes most range-free localization algorithms inaccurate. On the other hand, due to the power limitation of mobile sensor nodes (i.e., they are battery-operated) and high power consumption by communication, high communication cost will significantly reduce the network life time. For solving these two problems, in this paper, we use historical beacons (i.e., anchor nodes' announcements delivered in previous time slots) and received signal strength (RSS) to derive three constraints. By the aid of the three constraints, we introduce a low-communication-cost range-free localization algorithm (only one-hop beacon broadcasting is required). According to the theoretical analysis and simulation results, our three constraints can indeed improve the accuracy. Simulation results also show that our algorithm outperforms even in irregular-radio-signal environments. In addition, a hardware implementation running on sensor nodes, Octopus Xs, confirms theoretical analysis and simulation results.