Text-line extraction (TLE) from unconstrained handwritten document images is still considered an open research problem. Literature survey reveals that use of various rule-based methods is commonplace in this regard. But these methods mostly fail when the document images have touching and/or multi-skewed text lines or overlapping words/characters and non-uniform inter-line space. To encounter this problem, in this paper, we have used a deep learning-based method. In doing so, we have, for the first time in the literature, applied Generative Adversarial Networks (GANs) where we have considered TLE as image-to-image translation task. We have used U-Net architecture for the Generator, and Patch GAN architecture for the discriminator with different combinations of loss functions namely GAN loss, L1 loss and L2 loss. Evaluation is done on two datasets: handwritten Chinese text dataset HIT-MW and ICDAR 2013 Handwritten Segmentation Contest dataset. After exhaustive experimentations, it has been observed that U-Net architecture with combination of the said three losses not only produces impressive results but also outperforms some state-of-the-art methods.