In the two-minute appeal, The Duchess of Cambridge, who is Royal Patron of East Anglia's Children's Hospices, said she had seen first-hand the "transformational" work done for children and their families.
"Children's Hospice Week is a time to recognise, celebrate and support the inspirational work of those hospices."
"Children's hospices provide lifelines to families at a time of unimaginable pain. The support they give is vital.
"In order to carry out this wonderful work, our help is needed.
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The week's organisers said they were delighted by the duchess' support.
Barbara Gelb, chief executive of Together for Short Lives - which organises the annual week-long event - said she was "very excited" about Kate's support.
"I know this extraordinary backing will mean so much to all the UK's 49,000 children with palliative care needs and their families and will really help raise awareness of what these families need, today and in the future.
The video was recorded at Clarence House and shows the duchess speaking directly to camera.
Children's Hospice Week runs from April 26 to May 3.