Convolutional　Sparse　Coding　(CSC)　models　have　recently　gained　considerable　attention　in　signal　and　image　processing.　They　are　very　effective　in　image　denoising.　For　this　kind　of　model,　the　regularization　term　is　important　for　improving　the　performance　of　image　denoising.　This　paper　proposes　a　convolutional　sparse　representation　model　with　a　combination　of　gradient　and　elastic　net　penalty　terms　for　image　Gaussian　noise　denoising.　The　Combination　has　both　advantages　of　gradient　regularization　terms　and　elastic　net　regularization　terms　and　can　achieve　a　better　denoising　effect.　Experiments　show　that　this　combined　penalty　is　better　than　applying　gradient　penalty　and　net　elastic　penalty　separately　in　Gaussian　noise　denoising　application.　©　2021　IEEE.