Using a hybrid molecular dynamic and lattice Boltzmann simulation method, we investigate the flow-driven translocation of a diblock copolymer which is composed of a hydrophilic block and a hydrophobic block through a nanopore. Our results illustrate the nontrivial translocation dynamics of diblock copolymers. We find that the increase in the number of hydrophobic segments requires a larger critical flow rate and a reduced translocation time, which implies that the separation of diblock copolymers with different fractions of hydrophobic segments can be achieved by adjusting the flow rate. Our work deepens the understanding of copolymer translocation through a nanopore and provides an insight into designing related microscaled separation devices.