Localization is a fundamental problem in wireless sensor networks. Current localization algorithms mainly focus on checking the localizability of a network and/or how to localize as many nodes as possible given a static set of anchor nodes and distance measurements. In this paper, we study a new optimization problem, minimum cost localization problem, which aims to localize all sensors in a network using the minimum number (or total cost) of anchor nodes given the distance measurements. We show this problem is very challenging and then present a set of greedy algorithms using both trilateration and local sweep operations to address the problem. Extensive simulations have been conducted and demonstrate the efficiency of our algorithms.