In this paper, we propose a localization algorithm that uses the time difference of arrival (TDOA) and the angle of arrival (AOA). The problem is formulated in a hybrid linear matrix equation. TDOA and AOA measurements are used for estimating the target's position. Although it is known that the accuracy of TDOA based localization is superior to that of AOA based localization, TDOA based localization has a poor vertical accuracy in deteriorated geometrical conditions. This paper, therefore, proposes a localization algorithm in which the vertical position is estimated by AOA measurements and the horizontal position is estimated by TDOA measurement in order to achieve high location accuracy in three dimensions. In addition, the Lagrange multipliers are obtained efficiently and robustly. The simulation analysis shows that the proposed constrained linear squares (CLS) algorithm is an unbiased estimator, and that it approaches the Cramer-Rao lower bound (CRLB) when the measurement noise and the sensor's location errors are sufficiently small.