Large‐scale antenna arrays (LSAAs) are used to achieve satisfactory performance in 5G communications and radar systems. However, sidelobe suppression and nulls control of LSAAs are high‐dimensional nonlinear optimization problems owing to the large number of antenna elements. In this study, we formulate an optimization problem for joint sidelobe suppression and nulls control of large‐scale linear antenna arrays and propose particle swarm optimization with global search and population mutation (PSOGP) to solve this problem. PSOGP introduces global search and population mutation operators into conventional particle swarm optimization to improve performance in terms of convergence rate and accuracy in large solution spaces. Simulation results demonstrate that compared with other methods, the proposed PSOGP has better overall performance in joint sidelobe suppression and nulls control.