Abstract: To address the insufficient weak target detection performance of passive linear array under multi-target and low signal-to-noise ratio (SNR), a low-complexity adaptive Fourier integral method (LCA-FIM) is proposed. The proposed method designs multiple predefined window functions to generate weighted Fourier integral method outputs with diverse performance characteristics. Through low-complexity adaptive window function optimization, the optimal output is selected to achieve high gain, low sidelobe, and reduced computational complexity. Simulation results demonstrate that the LCA-FIM achieves superior resolution performance and robust background suppression capability under low SNR. The experimental results further demonstrate that, compared with conventional beamforming and adaptive beamforming methods, the LCA-FIM enhances resolution while suppressing background noise, thereby exhibiting robust weak target detection capabilities under multi-target and low SNR.