In a wireless sensor network, the localized sensors are essential for efficient management of the network. In recent years, we have seen the implementation of various localization schemes. Few schemes presume to use mobile beacon because it has many potentialities. Despite many potentialities, the mobile beacon-based localization schemes suffer from two significant problems. First, the shorter beaconing interval increases the communication overhead and degrades the network lifetime. Second, the radio propagation irregularity minimizes the uniform coverage. For a better network lifetime, we need to reduce the communication overhead. Similarly, consistent coverage is improved through better path planning and enhanced beaconing range. However, most of the proposed geometric schemes in literature fails to address both the problems with better localization accuracy. In this paper, we address the underlying impact of shorter beaconing interval and the radio propagation irregularity. The proposed scheme utilizes the geometric least square curve fitting method for localization (GLSCFL). The results show that the proposed method provides better localization accuracy than other geometric schemes.