Due to their low computational complexity, greedy pursuit algorithms are widely used in sparse signal reconstruction. An improved greedy iterative algorithm, called the expanded subspace pursuit, is proposed. By incorporating a simple backtracking technique, the proposed algorithm removes the mismatching atoms to refine the estimated support set effectively. Furthermore, the proposed algorithm can achieve blind sparse reconstruction even without the prior of the sparsity degree. Compared with other greedy algorithms, the proposed algorithm exhibits superior reconstruction accuracy and lower computational complexity. Finally, numerical results are presented to demonstrate the validity of the proposed algorithm.