This paper presents the implementation details of a parallel algorithm on graphics processing units (GPUs) to compute the optimal switching angles for the harmonic minimization in multilevel inverters with unequal dc voltage sources. Two algorithms, the Newton-Raphson method and the bisection method, and three different parallel implementations are investigated. Both algorithms considered have a low time complexity and offer a superior converging rate allowing for the real-time control of inverters with a very large number of levels. By exploiting the massively parallel architecture of GPUs, the execution time of the program is reduced significantly. The proposed parallel implementation offers a maximum speedup of 534× compared with a sequential execution on CPU, and allows for the calculation of the optimal switching angles for inverters with up to 1000 dc sources in less than 16.4 μs.