The multiple signal classification (MUSIC) algorithm, which was originally proposed to solve the direction of arrival (DOA) estimation problem in sensor array processing, has attracted much attention in recent years as a method to solve the multiple-measurement vectors (MMV) problem. While MUSIC reliably reconstructs the row sparse signals in the full row rank case, it performs poor in the rank deficient case. In order to overcome the limitation of MUSIC, we propose a robust greedy algorithm, henceforth referred to as an MMV orthogonal least squares (MMV-OLS) algorithm, for the MMV problem. Our analysis shows that in the full row rank case, MMV-OLS guarantees exact reconstruction of any row K-sparse signals from K + 1 measurements, which is in fact optimal since K + 1 is the smallest number of measurements to recover the row K-sparse matrices. In addition, we show that the recovery performance of MMV-OLS is competitive even in the rank deficient case by providing empirical results.