Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum have more information and are capable to reduce the Gaussian noises. In this paper, a kind of spectrum estimation method for direction-finding is presented based on the eigen-structure analysis of the fourth-order cumulants. The algorithm is derived and its performance is illustrated by both the computer simulations and the experiments of the direction-finding system. The obtained results demonstrate that the fourthorder cumumlant-based method outperforms the traditional direction-finding method, especially when the noise is unknown coloured one.