In order to describe the highly scattered property of millimeter wave (mmWave) multiple-input multiple-output (MIMO) channels, the existing high resolution frequency domain space-alternating generalized expectation-maximization (FD-SAGE) algorithm is studied and extended to three-dimentional (3D) MIMO case by including the estimation of elevation angles. The signal model and estimation procedure are described in detail and the capability of the proposed algorithm is verified in both synthetic and real measurement environments. Firstly, the performance of the proposed 3D FD-SAGE algorithm is evaluated in simulated single-input multiple-output (SIMO) channels. The estimation results match well with the parameter settings. Secondly, the impact of antenna array configuration and signal-to-noise ratio (SNR) on the capability of the proposed algorithm is also analyzed. It is found that systems with large antenna array size and high SNR exhibit excellent performance in angular estimation. Finally, 60 GHz mmWave indoor channel measurements are carried out and the channel parameters are estimated using the proposed 3D FD-SAGE algorithm.