This paper presents an approach for the estimation of two-directional (2D) direction-of-arrival (DOA) of more sources than sensors using an Acoustic Vector Sensor (AVS). The approach is developed based on Khatri-Rao (KR) product by exploiting the subspace characteristics of the time variant covariance matrices of the uncorrelated quasi-stationary source signals. An AVS is used to measure both the acoustic pressure and pressure gradients in a complete sound field and the DOAs are determined in both horizontal and vertical planes. The identifiability of the presented approach is studied using computer simulations. It is demonstrated that the 2D DOAs of six speech sources are successfully determined using the new approach, which is significantly superior over the existing linear array approach.