Based on moving least squares, an algorithm of trajectory tangent azimuth calculation is presented in this paper. The feasibility of the algorithm is tested by measured data and the setting of key parameters including dilatation parameter and weight function is discussed. The results show: the algorithm is practical and can be applied to small bended trajectory; the value of dilatation parameter should satisfy the requirement of calculation, but it should not be too big; the precision of trajectory fitting can be promoted by weight function but the precision of azimuth will not be affected.