Compressive sensing (CS) based estimation technique utilizes a sparsity promoting constraint and solves the direction-of-arrival (DOA) estimation problem efficiently with high resolution. In this paper a grid free CS based DOA estimation technique is proposed, which uses sequential multiple snapshot data. Conventional CS technique suffers from a basis mismatch issue, while grid free CS technique is relieved of basis mismatch problem. Moreover, when the DOAs are stationary, multiple snapshot processing provides stable estimates over fluctuating single snapshot processing results. For multiple snapshot processing, the generalized version of total variation norm (group total variation norm) is implemented to impose a common sparsity pattern of multiple snapshot solution vectors in a continuous angular domain. Furthermore, an extended version is proposed using the singular value decomposition technique to mitigate computational complexity resulting from a large number of multiple snapshots. Data from SWellEx-96 are used to examine the proposed method. From the experimental data, it was observed that the present method not only offers high resolution even when the sources are coherent, but also the basis mismatch in the conventional CS method can be avoided.