Recently, Ultra HDTV (UHDTV) services become popular over satellite and on the internet. On the contrary, there are tremendously huge volume of High Definition Television (HDTV) and Standard Definition Television (SDTV) contents stored in broadcasting companies and storage devices. In this paper, we propose a color space conversion (also known as gamut mapping) method from BT. 709 (used for current HDTV broadcast) to BT. 2020 (used for UHDTV broadcast), which estimates and restores lost color information. It learns an end-to-end conversion method from BT. 709 image to BT. 2020 image with restoring lost color information using Convolutional Neural Network (CNN). By experiments, we confirm that our method can achieve 2.31dB gain against the conventional method on average.