In general, precise attitude information is required to control a ground simulator, which is designed to simulate attitude control of spacecraft. Two algorithms are well-known to determine the attitude through two or more observation vectors. One is the deterministic method, such as the TRI-axis Attitude Determination (TRIAD) algorithm, and the other is the optimal method, such as the QUaternion ESTimator (QUEST) algorithm. This paper suggests a new efficient attitude determination algorithm, which the authors name an algorithm "Averaging TRIAD." First, it is transformed from the attitude matrix to the attitude angle vectors to maintain orthogonal constraints during calculation. Second, the covariance matrix is used instead of the variance and then it is applied to an unbiased minimum variance formula for more accurate solutions. Finally, the authors suggest a methodology to determine the attitude when more than three measurements are given. The performance of the Averaging TRIAD algorithm upon the combination of different sensors, which are fixed to the ground simulator, is investigated by numerical simulation in terms of standard deviations and computational time.