Millimeter wave (mmWave) is capable of supporting ultra-high system performance due to its spatial diversity from directional transmission techniques in fifth generation (5G) wireless networks. Improved by the beamforming, mmWave could be applied to potentially achieve more accurate indoor positioning. Due to impermeability and high path loss of mmWave, most of transmission is operated under line-of-sight (LoS) conditions. In this paper, we propose beam-based midline intersection positioning (BMIP) and advanced beam scaling positioning (ABSP) for indoor positioning. Two mmWave access points (APs) are employed for performing positioning under LoS conditions. The user equipment (UE) will receive downlink information of angle-of-departure (AoD) and corresponding signal-to-noise-ratio (SNR) values from two APs, respectively. We have evaluated our proposed BMIP and ABSP indoor positioning algorithms via both mmWave ray-tracing based simulation and experimental implementation using commercialized 60 GHz transceivers. The results demonstrate that our proposed positioning algorithms could achieve the centimeter-level estimation errors.