Detecting and recognizing the license plates in hazy or foggy weather conditions is a challenging task. The paper derived a mathematical MAC-Generative Network (MAC-GN) using Unpaired Multi-head Attention mechanism based on CycleGAN. Unlike the basic generator architecture of cycleGAN, the derived MAC-GN adds a multi-head attention mechanism to the encoder and the decoder for generating new sample images. CycleGAN uses a cycle-consistency loss to enforce the mapping between the noisy and clear license plate images. The derived MAC-GN used patch GAN as discriminator system with the ability to generate high-quality, high-resolution images with fine details and textures. The MAC-GN is evaluated using three image quality assessment metrics: Peak signal-to-Noise Ratio, Structural Similarity Index Measure and Perception based Image Quality Evaluator. The experimental result shows that the derived MAC-GN generates a restored, haze free license plate images with a natural image view. The results have shown an improvement of 13.1% on PSNR and 10.12% on SSIM.