FIG. 1 is a front, top and side perspective view of an insect killing device showing my new design; FIG. 2 is a front view thereof; FIG. 3 is a rear view thereof; FIG. 4 is a side view thereof; FIG. 5 is an opposite side view thereof; FIG. 6 is a top view thereof; FIG. 7 is a bottom view thereof; and, FIG. 8 is a detailed view of a bottom surface of the top portion thereof.