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Using the target signal in the spatial distribution of sparse, this paper puts forward a Khatri-Rao(KR) product based on virtual array and signal subspace joint sparse representation of single snapshot DOA estimation method. The method uses a single snapshot sampling data, constructs the two-way virtual array data, and the covariance matrix of the virtual array data for KR product transformation process, and then to reconstruct the order of data after vectorization, by using the large singular values of reconstruction matrix left singular vectors of the corresponding to estimate the signal subspace; Finally, using convex optimization toolbox for sparse matrix model of quadratic convex programming optimization solution, get high accuracy DOA estimate. Simulation experiments verify the effectiveness of the algorithm, under the low SNR has higher estimation accuracy than traditional MUSIC,SVD and OMP algorithm.