Abstract: To address the issues of significant spectral distortion and poor kurtosis transfer efficiency in conventional non-Gaussian signal generation methods, a high-precision algorithm based on amplitude–phase spectrum recombination is proposed. Its effectiveness is validated through both simulation and experimental studies. The method constructs an innovative iterative framework wherein the amplitude spectrum of the reference signal is strictly preserved, while the phase spectrum is reconstructed using time-domain modulations. This enables the introduction of target non-Gaussian characteristics without altering the spectral properties. Comparative simulation results demonstrate that, unlike traditional amplitude modulation and Hermite polynomial-based methods, the proposed approach exhibits substantial advantages in spectral fidelity: across various kurtosis levels, the relative root mean square error (RRMSE) of the power spectral density is consistently maintained at 1.28%, in contrast to 39.11% for conventional methods. Furthermore, the consistency of system responses is significantly improved, with the coefficient of variation of response metrics remaining below 0.1%, compared to over 17% for existing methods. In addition, the proposed method enhances the efficiency of kurtosis transfer in dynamic responses, allowing effective propagation of non-Gaussian features. Overall, the results confirm that the proposed method achieves a decoupling of kurtosis control and spectral preservation, overcoming key limitations of existing techniques and offering a high-precision, high-fidelity, and robust solution for simulating non-Gaussian shock environments in engineering applications.