In mobile wireless sensor networks, sensors move in the monitored area at any direction and at any speed. Unlike many other networking hosts, sensor nodes do not have global addresses. Very often they are identified by using a location-based addressing scheme. Therefore, it is important to have the knowledge of the sensor location indicating where the data came from. In this paper, we design three mobility-pattern based localization update algorithms. Specifically, we divide sensor movements into three states, Pause, Linear, and Random. Each state adopts different localization update algorithms. Analytical and simulation results are provided to study the localization cost and location accuracy of the proposed localization-update algorithm in different mobility patterns. The analysis to these results indicates that the localization cost is minimized and the location accuracy is improved.