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Sparse signal approximations have become a new tool in signal processing with wide ranging applications from source separation to signal acquisition. Recently, many algorithms for sparse signal reconstruction have been developed, however, greedy algorithms, such as Orthogonal Matching Pursuit algorithm, can have better performance than the other algorithms. Approximate orthogonal matching pursuit algorithms, such as gradient pursuit algorithm and conjugate gradient pursuit algorithm, can lead to fast approximations to Orthogonal Matching Pursuit. In this paper Newton pursuit algorithm for sparse signal reconstruction is proposed. The algorithm is a kind of directional pursuit algorithms with the same computational complexity compared to orthogonal matching pursuit algorithm, but it can have better performance than approximate orthogonal matching pursuit algorithms.