A new and distinct Torenia plant named `Dancatblue` particularly characterized by the combined features of pale violet-blue petals with violet-blue blotches on the side petals surrounding the corolla, and the lower petal with a centered yellow-green blotch near the base; bush, cascading, vigorous growth habit which maintains a compact, rounded growth habit; densely branched plant, gracefully cascading from hanging baskets; early flowering and year round blooming in moderate climate; suitable as an annual for hanging pots outdoors under partial shade; and good weather tolerance.