The grounded electrical source airborne transient electromagnetic (GREATEM) system is widely used in groundwater resources detection, geothermal resource detection, geological structure detection, and other fields due to its wide detection range, high detection efficiency, and high resolution. The field data received by the GREATEM system is easily affected by various noises, such as instrument system noise, power frequency noise, sferics noise, and other noise, which reduce the data signal-to-noise ratio (SNR) and affects the data interpretation accuracy. This paper proposes a singular spectrum analysis (SSA) for the GREATEM data de-noising in response to this problem. First, we calculate the electromagnetic response of a uniform half-space using a GREATEM system with an electrical source to verify the effectiveness of the SSA algorithm for GREATEM data de-noising. To determine the appropriate parameters for SSA, we propose a particle swarm optimization algorithm to choose the window length. Later, SSA is used to decompose a synthetic quasi-two-dimensional earth model of GREATEM data. After SSA, the SNR of the reconstructed signal increased by 36 dB, and the RMSE does not exceed 4.9 × 10−6, which verifies the feasibility of the SSA for de-noising GREATEM data. Finally, through field measurement data processing, the effectiveness of the method is further confirmed.