A new Anthurium plant named ‘ANTHFUNCNI’ particularly distinguished by having concave, weakly blistered and medium glossy, deep red, cordate, and durable spathes that retain the original color for a very long period of time, green and ovate-cordate, concave, durable leaves, white spadices with yellow-green tips, early and rich flowering continuously throughout the year, and a plant height of 39.0 cm to 44.0 cm is disclosed.