In this letter, a new analysis technique for finding the convexity of iterative maximum likelihood (IML) methods for direction-of-arrival (DOA) estimation is presented. The proposed technique can pave the way in avoiding the local solution when the IML methods are utilized to estimate DOA, especially for the scenarios of array with large antennas. From the derivation, we can see that as long as the initial DOA belongs to the approximate convex range estimated by our proposed technique, the IML methods can estimate the DOA very well without entering into local minima, which is particularly true for the large arrays. Furthermore, numerical experiments show us the results tallied well with our theoretical derivations.