I can identify. After never being particularly scared of death and a good many depressive times when I longed for it, I suddenly found myself in my thirties being scared witless by the prospect.

So here are a few thoughts to help get past this paralyzing and unnerving fear.
Obviously, Catholic tradition is not to be scared of death. But we are only human, and our minds and bodies are very changeable. Feelings come and go. It’s what you do with them that counts. There have been saints who have found themselves with a paralyzing fear of death. The proper answer is to love God and trust Him to help you through the fear.
First of all, brooding isn’t a good thing. Make sure your grandmother has enough going on to occupy her time. Is she getting enough sleep, exercise, food, visits, fun, creative projects, etc.? Is she really afraid that she doesn’t matter to anyone and nobody will care when she’s gone? Depression or illness can cause all kinds of “bad thoughts” and fears. If you have better things to think about, the bad thoughts will be forgotten.
Second, all Christians are supposed to be “in training” for death, or rather, for the afterlife. Old people are no exception to this. The Catholic tradition includes many spiritual training guides.
If your grandmother is really really afraid of death, you probably want to go slowly, with books more about increasing one’s love of God and intensifying one’s prayer life. Things like St. Therese’s The Story of a Soul, St. Teresa of Avila’s book The Interior Castle, Thomas a Kempis’ The Imitation of Christ, The Practice of the Presence of God, or St. John of the Cross’ beginners’ book The Ascent of Mount Carmel. Obviously the Gospels would also help a lot, or consoling prayers like the Divine Mercy Chaplet or the Rosary.
OTOH, if your grandmother’s the kind who’s frustrated by her fear and would rather go straight at things, St. Robert Bellarmine’s book The Art of Dying Well is very helpful. Most translations include only the first part (for people not dying soon), which may be more tactful. (The second part is for people who are pretty sure they’re going to be dying pretty soon, like in the next few months or days.) There’s also books by him on consoling topics like the communion of the saints, etc. He wrote most of these devotional books for ordinary people when he was old himself.
And as everybody else has said, obviously talking to a priest, getting to Mass or at least receiving the Eucharist, adoration, etc. will help.