Yes. While it’s not the usual situation that someone in a younger generation gives gifts to someone in the older generation, there’s no tax rule barring this. In fact, under tax law there’s no bar to gifts being made by minors.
The tax on the investment income in excess of $1,700 (may change after 2007) of a child under age 18, based on the parents’ marginal tax rate and computed on Form 8615.