You Do Need power plug adapter while traveling from Christmas Island to Greenland.

Here is Why You Need An Adapter

The outlet and plug type used in Greenland are C, E, F and K and in Christmas Island is I. This is how they look like.

Christmas Island

In Christmas Island, outlets of type I are in use.

Type I

Greenland

In Greenland, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K