A fast sparse covariance-based fitting algorithm with the non-negative least squares (NNLS) form is proposed for the direction of arrival (DOA) estimation. The Khatri-Rao product of the array manifold of the uniform linear arrays is utilized to achieve the dimension reducing transformation after vectorizing the array covariance matrix. Furthermore, the DOA estimation problem is derived as a NNLS problem by using the non-negative property of the spatial spectrum, which can be solved by some efficient solvers. Numerical experiments show that the proposed method can obtain high resolution with a competitive computational complexity, as well as works in the presence of coherent sources.