The Queen has been hosting on the first day of his state visit, and carefully picked out a gift for the US leader, but the president was caught out when he failed to recognise a gift he gave the monarch last year.
The monarch presented Mr Trump with a specially decorated book written by war-time prime minister, Winston Churchill.
The crimson book features an EIIR cypher in gold on the front, silk endpapers and hand-sewn headbands in the colours of the US flag with all pages in gilt.
But, the president was left scratching his head when he failed to recognise a gift he had bought the Queen in July last year.
Britain's head of state took the president and First Lady Melania Trump around an exhibition of American artefacts at Buckingham Palace.
However when they came across a thoroughbred in polished pewter, the US leader did not know the artwork was his gift to the Queen when they met in July last year - yet Mrs Trump did.
Tim Knox, director of the Royal Collection who joined the Queen during the tour, said Mr Trump gave the monarch the horse when he had tea with her at Windsor Castle.
He added that when Mr Trump was asked if he recognised it, he said "no" but "the First Lady did recognise it, which is rather nice".
Mr Knox joked: "But one horse looks very much like another."
She also gave Mr Trump a three-piece Duofold pen set - a fountain pen, rollerball pen and ball point pen with EIIR cypher - using the obsidian design, exclusively made for the Queen.
First Lady Melania Trump was presented with a specially commissioned silver box with a handcrafted enamel lid.
Its royal blue decoration featured roses, thistles and shamrocks to represent the ceiling of the palace music room.
Donald Trump’s present to the Queen has not yet been revealed.