If the direction of arrival (DOA) of a source is perturbed due to some reasons in a statistical way as in the environment of wireless mobile communications, a new model appropriate for such environment should be used instead of the point source model. In this paper, an angle-perturbed source model is proposed and an estimation method based on the eigendecomposition technique is investigated under the model. The asymptotic distribution of the estimation errors is obtained to see the statistical properties.