Film cooling injection from discrete circular holes is widely used in gas turbines to reduce the heat load of the turbine blades. Placing a special designed structure upstream or downstream, the circular hole has been proven to be a new effective way to improve cooling effectiveness in recent years. In the present study, numerical investigations were performed on a row of circular holes over a flat plate with crescent-shaped blocks. Totally seven configurations without block, with blocks located at six streamwise positions including 6 times, 5 times, 4 times of hole diameter upstream, and 0.5 times, 1.5 times, 2.5 times of hole diameter downstream at blowing ratios of 0.5-1.5 were tested symmetrically. The Reynolds-averaged Navier-Stokes equations with the k-ω shear-stress transport model were solved. Flow fields, cooling effectiveness and aerodynamic losses were analyzed in detail. Although with different generation mechanism, additional vortex pair opposite to the counter-rotating vortex pair was generated by placing either an upstream or downstream block, which could finally improve the coolant lateral coverage and thus cooling effectiveness. The cooling performances and aerodynamic losses between configurations without block and with blocks at six streamwise positions were then compared. Finally, the optimal streamwise position of the block was recommended at various blowing ratios.