A curved liquid crystal display panel and a curved liquid crystal display device are disclosed. The curved liquid crystal display panel comprises: two substrates curved towards a same direction with liquid crystals filled therebetween to form a curved liquid crystal layer; and a transparent layer covering an outer surface of a glass of at least one of the substrates, a stress-optical coefficient of the glass of the substrate and a stress-optical coefficient of the transparent layer at a same side of the liquid crystal layer have opposite signs, wherein the outer surface of the glass of the substrate is a surface of the glass of the substrate away from the liquid crystals. The curved liquid crystal display device comprises the curved liquid crystal display panel. The optical rotation effects of the glass of the substrate and the transparent layer located at the same side of the liquid crystal layer are opposite from each other, optical delay thereof are counteracted by each other. Display effect of the curved liquid crystal display panel and the curved liquid crystal display device according to embodiments of the invention is improved largely.