This paper studies the problem of determining sensor locations in a large sensor network using only relative distance (range) measurement. Based on the barycentric coordinate representation, our work generalizes the DILOC algorithm in an asynchronous communication environment with time delays and packet losses. Firstly, an asynchronous communication protocol based on barycentric coordinate is developed, and the distributed localization algorithm is mathematically modeled as a linear difference equation with time-varying delays. Next, by using the extended delay graph theory, we prove that the asynchronous iterative model is globally convergent to the true coordinates if: 1) time interval between any two consecutive update time instants is bounded above and below. 2) communication delays and successive packet losses between sensors are finite. Finally, simulation examples are provided to demonstrate the effectiveness of the theoretical result.