A new and distinct Torenia plant named `DANMOON14` characterized by having shiny green foliage, doted with plenty of delicate, funnel form, cup-shaped flowers with petals in shades of violet, purple and light purple with a yellow blotch on lower petal; vigorous growth habit; densely, compact branching habit which gracefully semi-cascading from hanging baskets; early flowering response and stays in full bloom in moderate climate; suitable as an annual for hanging pots outdoors under partial shade; and good weather tolerance with a preferred temperature range of 15.degree. C. to 25.degree. C.