To effectively process impulse noise for narrowband powerline communications (NB-PLCs) transceivers, capturing comprehensive statistics of nonperiodic asynchronous impulsive noise (APIN) is a critical task. However, existing mathematical noise generative models only capture part of the characteristics of noise. In this study, we propose a novel generative adversarial network (GAN) called noise generation GAN (NGGAN) that learns the complicated characteristics of practically measured noise samples for data synthesis. To closely match the statistics of complicated noise over the NB-PLC systems, we measured the NB-PLC noise via the analog coupling and bandpass filtering circuits of a commercial NB-PLC modem to build a realistic dataset. To train NGGAN, we adhere to the following principles: 1) we design the length of input signals that the NGGAN model can fit to facilitate cyclostationary noise generation; 2) the Wasserstein distance is used as a loss function to enhance the similarity between the generated noise and training data; and 3) to measure the similarity performances of GAN-based models based on the mathematical and practically measured datasets, we conduct both quantitative and qualitative analyses. The training datasets include: 1) a piecewise spectral cyclostationary Gaussian model (PSCGM); 2) a frequency-shift (FRESH) filter; and 3) practical measurements from NB-PLC systems. Simulation results demonstrate that the generated noise samples from the proposed NGGAN are highly close to the real noise samples. The principal component analysis (PCA) scatter plots and Fréchet inception distance (FID) analysis have shown that NGGAN outperforms other GAN-based models by generating noise samples with superior fidelity and higher diversity.