This paper proposes a fast learning-based method for direction-of-arrival (DOA) estimation of multiple broadband far-field sources. The processing procedure involves two steps. First, a beamspace preprocessing which has the property of frequency invariant is applied to the array outputs to perform focusing over a wide bandwidth. By converting the outputs from the element-space to beamspace in this step, the computation can be reduced through adjusting the number of beamformers. In the second step, a hierarchical deep neural network is employed to achieve classification, which can output the DOA estimates. Simulation results verify the effectiveness of the proposed method.