In order to reduce the complexity of signal reconstruction algorithm, and reconstruct the signal with unknown sparsity, a new algorithm named One Projection Subspace Pursuit (OPSP) was proposed. Firstly, the upper and lower bounds of the signal's sparsity were determined based on the restricted isometry property, and the signal's sparsity was set as their integer middle value. Secondly, under the frame of Subspace Pursuit (SP), the projection of the observation onto the support set in each iteration process was removed to decrease the computational complexity of the algorithm. Furthermore, the whole signal's reconstruction rate was used as the index of reconstruction performance. The simulation results show that the proposed algorithm can reconstruct the signals of unknown sparsity with less time and higher reconstruction rate compared with the traditional SP algorithm, and it is effective for signal reconstruction.