Silicon photonics has become the key enabling technology in many sensor applications including light detection and ranging (LiDAR) systems because of its high integration, chip-scale footprint and CMOS-compatible process. Thanks to these advantages, optical phased array (OPA) based on silicon photonics has emerged as a solid-state LiDAR solution to replace mechanical LiDAR counterpart. In such a system, optical loss from each component of the OPA devices should be minimized, while the radiation efficiency from the radiators of the OPA devices should be maximized for extending the power budget of the LiDAR system. These components can improve their performances through the recently emerged inverse design method. In this study, we designed a novel grating structure which is one of the components of OPA and allows wide-band and high coupling efficiency of light using inverse design approach with the particle-swarm-optimization method. Considering Silicon-On-Insulator (SOI) platform with 220 nm thickness, the configuration of the grating structure is determined by the finite number of particles so that the height and width of the corrugations are optimized based on the objective of boosting the out-of-plane radiated power amount. Highly efficient and vertical emission was obtained using finite-difference-time-domain calculation in telecommunication window centered at around 1550 nm. Including additional constraints in the inverse design will allow the realization of multitude spatial field profiles of the radiated light that may have an important contribution for OPA, sensing, imaging, lasers and optical interconnection.