Communication with unlicenced 60-GHz band is attractive for wireless networks since a free-of-charge bandwidth of 7 GHz is available. The antenna array, conducting transmitter/receiver beamforming, is often used to enhance the transmission range. However, to conduct beamforming, the transceivers have to know the angles of signal arrival. Many angle-of-arrival (AoA) estimation algorithms are well known. Unfortunately, most of them are developed for digital arrays, requiring an analog-to-digital-converter (ADC) and a digital-to-analog converter (DAC) for each antenna element. For an array with a large number of antennas, the implementation cost will be very high. Recently, hybrid antenna array, in which multiple antennas share an ADC/DAC, was proposed as a low-cost solution. However, the existing AoA estimation algorithms for hybrid arrays can only support one AoA; their applications are then limited in multipath indoor environments. In this paper, we propose new AoA estimation algorithms to solve the problem. Using an augmented beam-space approach, we extend the use of the well-known AoA estimation algorithms, MUSIC and ESPRIT developed for digital arrays, to the scenario of hybrid antenna arrays. Simulations show that the proposed algorithms, although developed for hybrid arrays, can have similar performance as MUSIC and ESPRIT in digital arrays.