In this paper, we propose a simulation-based evolutionary approach for designing low noise amplifier (LNA) integrated circuits (ICs). Based on a genetic algorithm (GA), the Levenberg-Marquardt (LM) method, and a circuit simulator, the simulation-based evolutionary approach is developed for design optimization of LNA circuits. For a given LNA circuit, the simulation-based evolutionary approach simultaneously optimizes the electrical specifications, such as S11, S12, S21, S22, K factor, the noise figure, and the input third-order intercept point in the process between simulation and optimization. First of all, the necessary parameters of the LNA circuit for circuit simulation are loaded. By solving a set of nonlinear ordinary differential equations, the circuit simulator will then be performed for the circuit simulation and specification evaluation. Once the specification meets the aforementioned seven constraints, we output the optimized parameters. Otherwise, we activate the GA for the global optimization; in the meanwhile, the LM method searches the local optima according to the results of the GA. We then call circuit simulator to compute and evaluate newer results until the specification is matched. In numerical experiment, 10 parameters of the LNA circuit including device configuration and biasing condition are optimized with respect to the constraints. The design of LNA circuit is with 0.18 μm metal-oxide-silicon filed effect transistors. Benchmark results also computationally confirm the robustness and efficiency of the proposed method. This simulation-based evolutionary approach, in general can be applied to optimal design of other analog and radio frequency circuits. We believe that this systematical approach will help IC design optimization, and benefit computer-aided design of wireless communication system-on-a-chip.