This paper presents a novel algorithm for recovering missing phasor measurement unit (PMU) data. Due to the low-rank property of PMU data, missing measurement recovery can be formulated as a low-rank matrix-completion problem. Based on maximum-margin matrix factorization, we propose an efficient algorithm, alternating direction method of multipliers (ADMM), for solving the matrix completion problem. Compared to existing approaches, the proposed ADMM based algorithm does not need to estimate the rank of the target data matrix and provides better performance in computation complexity. Since PMU data are transferred through insecure and delayed communications, we consider the case of measurements missing from all PMU channels in several sampling instants and provide the strategies of reshaping the matrix composed by the received PMU data for the recovery. Numerical results using real PMU measurements from State Grid Jiangsu Electric Power Company illustrate the effectiveness and efficiency of the proposed approaches.