We study drag reduction of a uniform flow over a flat surface due to a series of rectangular microgrooves created on the surface. The results reveal that making grooves on the surface usually leads to the generation of secondary vortices inside the grooves that, in turn, decreases the friction drag force and increases the pressure drag force. By increasing the thickness of the grooves to the thickness of the obstacle, the pressure drag increases due to the enhancement of the generated vortices and the occurrence of separation phenomenon and the friction drag reduces due to a decrease of the velocity gradient on the surface. In addition, by increasing the grooves depth ratio, the pressure drag coefficient decreases and the friction drag coefficient increases. However, the impact of the pressure drag coefficient is higher than that of the friction drag coefficient. From a specific point, increasing the groove depth ratio does not effect on decreasing the total pressure drag of the plate. Therefore, creating the grooves in flat surfaces would reduce the total drag coefficient of the plate if the thickness of the grooves does not exceed a specific size and the depth of the grooves is chosen to be sufficiently large. The lattice-Boltzmann method (LBM) is used and the optimal reduction of the drag coefficient is calculated. It is found that for the width ratio equal to 0.19 and the groove depth ratio equal to 0.2548, about 7% decrease is achieved for the average total drag.