Compressive sensing (CS) is perceived as a breakthrough in sampling theory, as it proves that sparse signals can be reconstructed from fewer samples than required by the Shannon-Nyquist theorem. However, CS can hardly be applied to real-time applications because reconstruction algorithms are computationally demanding. To tackle this problem, in this paper, we propose a new high-speed architecture for implementing the orthogonal matching pursuit (OMP), which is one of the most popular algorithms for CS reconstruction. Specifically, a novel pipelined systolic architecture and an optimized scheduling strategy are proposed. From the synthesis results, we find that the proposed design takes 1.638 µs to reconstruct 16-sparse signal, which is 19.2 times faster than the existing VLSI implementation of the OMP.