This letter considers the design of measurement matrices with low complexity, easy hardware implementation and good sensing performance for practical compressed sensing applications. We construct a class of sparse binary measurement matrices from protograph Low-density parity-check (LDPC) codes, which can satisfy these features simultaneously. The optimal performance of proposed matrices is analyzed from the mutual coherence aspect. Moreover, we obtain a sufficient condition for optimal construction of the matrices using proposed algorithm. Simulation experiments also demonstrate that orthogonal matching pursuit (OMP) algorithm performs better using the constructed matrices as compared with several state-of-the-art measurement matrices, such as random Gaussian matrices.