This paper presents an efficient wideband two-dimensional direction-of-arrival (DOA) estimation for an L-shaped microphone array. We propose a way to construct a wideband sample cross-correlation matrix without any process of DOA preliminary estimation, such as beamforming technique, by exploiting sample cross-correlation matrices of two different frequencies for all frequency bins. Subsequently, wideband DOAs can be estimated by using this wideband matrix along with a scheme of estimating DOA in a narrowband subspace method. Therefore, a contribution of our study is providing an alternative framework for recent narrowband subspace methods to estimating the DOA of wideband sources directly. It means that this framework enables cutting-edge techniques in the existing narrowband subspace methods to implement the wideband direction estimation for reducing the computational complexity and facilitating the estimation algorithm. Theoretical analysis and effectiveness of the proposed method are substantiated through numerical simulations and experiments, which are performed in reverberating environments. The results show that performance of the proposed method performs better than others over a range of signal-to-noise ratio with just a few microphones. All these advantages make the proposed method a powerful tool for navigation systems based on acoustic signal processing.