A novel algorithm for estimating 2D Angle-of-arrival of spatial signals using L array is presented in this paper, which is based on sparse decomposition of signal against the deficiencies of traditional DF algorithms and sub-space algorithms in narrowband case. The former methods are widely used in actual applications. However, they have many drawbacks such as low-resolution, bad robustness and etc. The latter ones which base on subspace method have gained great interest in the past two decades. What we know about this kind of methods are their super-resolution quality and their weaknesses as well, e.g. constrained by the number of elements, behaving badly when correlativity of sources grows. Approach proposed in this paper fist constructs atom-dictionaries according to system models and then projects observations of L array onto dictionaries, finally obtains AOAs by solving least squares problems. In the end of the paper, this approach is applied into wideband case to estimate parameters of chirp sources. Numerical simulations have proved the effectivity of the algorithm and good performance in low signal-to-noise ratio (SNR) regime.