Estimation of three-dimensional (3-D) direction-of-arrival angles (DOA) has received a significant amount of attention over the last several decades. It has also played an important role in array signal processing areas such as radar, sonar, radio astronomy, and mobile communication systems. In this work, we extend our original approximate maximum likelihood (AML) algorithm which has already been provened to work very well under a two-dimensional scenario, to work for a three-dimensional case. The main challenge in this extension is to have good accuracy of DOA estimation for all possible azimuth and elevation angles, while keeping the complexity of algorithm still as low as possible. We will show that for some specific subarray configurations named as isotropic arrays, we can achieve this goal very well.