An improved independent component analysis (ICA) method is proposed to address the issues of amplitude amplification and poor separation performance in blind source separation of rain sound signals using the traditional fast independent component analysis (FASTACA) method based on objective functions such as negative entropy. Traditional complex objective functions (negative entropy, kurtosis, etc.) are no longer used. Instead, we choose non-Gaussianity based on maximizing the signal. A combination of the hyperbolic cosine function and the logarithmic function for nonlinear transformation is utilized. Meanwhile, we reconstruct the objective function based on the mean difference square between the source signal and the separated signal. To improve the algorithm′s running, convergence speed, and optimization ability, the particle swarm optimization (PSO) algorithm is utilized instead of the traditional gradient descent method. Its fast global search ability is adopted to optimize the objective function, effectively avoiding the problem of ICA getting trapped in local optima during the iteration process. After obtaining the optimal solution mixing matrix, the rain sound mixed signal and extracting a purer rain sound signal are separated. The experimental results show that the improved ICA can meet the requirements of blind source separation, and the separation index (PI) reaches a level of 10-2. To further evaluate the effectiveness and stability of the proposed algorithm, blind source separation experiments are conducted in mixed scenarios of different types of rain sounds and environmental noise. The results show that the improved ICA algorithm can effectively separate and recover the source rain sound signal in mixed signals under different environmental noise backgrounds. In addition, comparing the ICA algorithm with the improved objective function and the FASTACA algorithm based on negative entropy, the proposed algorithm not only effectively solves the amplitude expansion problem caused by the FASTACA algorithm, but also converges faster, reducing the mean square error (MSE) by two orders of magnitude. The signal distortion ratio (SDR) under the rain sound type is increased by nearly 20 dB.