Prince Louis reached the milestone on Tuesday.
The photos, taken by Kate, show him playing in the garden of the family's home in Norfolk, on England's eastern coast.
Louis is fifth in line to the throne, behind his grandfather, Prince Charles, his father, Prince William, his brother, Prince George, and his sister, Princess Charlotte.
Louis is a great-grandson of Queen Elizabeth II, who turned 93 on Sunday.
He has largely been kept out of the public eye since he was born.
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