Two-dimensional (2-D) optical phased arrays (OPAs) usually suffer from limited scan ranges and small aperture sizes. To overcome these bottlenecks, we utilize an aperiodic 32 × 32 grid to increase the beam scanning range and furthermore distribute 128 grating antennas sparsely among 1024 grid points so as to reduce the array element number. The genetic algorithm is used to optimize the uneven grid spacings and the sparse distribution of grating antennas. With these measures, a 128-channel 2-D OPA operating at 1550 nm realizes a grating-lobe-free steering range of 53° × 16°, a field of view of 24° × 16°, a beam divergence of 0.31° × 0.49°, and a sidelobe suppression ratio of 9 dB.