In this paper, we propose a lightweight U-net architecture neural network model based on Dark Channel Prior (DCP) for efficient haze (fog) removal with a single input. The existing DCP requires high computational complexity in its operation. These computations are challenging to accelerate, and the problem is exacerbated when dealing with high-resolution images (videos), making it very difficult to apply to general-purpose applications. Our proposed model addresses this issue by employing a two-stage neural network structure, replacing the computationally complex operations of the conventional DCP with easily accelerated convolution operations to achieve high-quality fog removal. Furthermore, our proposed model is designed with an intuitive structure using a relatively small number of parameters (2M), utilizing resources efficiently. These features demonstrate the effectiveness and efficiency of the proposed model for fog removal. The experimental results show that the proposed neural network model achieves an average Peak Signal-to-Noise Ratio (PSNR) of 26.65 dB and a Structural Similarity Index Measure (SSIM) of 0.88, indicating an improvement in the average PSNR of 11.5 dB and in SSIM of 0.22 compared to the conventional DCP. This shows that the proposed neural network achieves comparable results to CNN-based neural networks that have achieved SOTA-class performance, despite its intuitive structure with a relatively small number of parameters.