The £1 billion warship carried out the firing exercise, which was designed to simulate a projectile attack on the ship, off the coast of Scotland.
The missile flew at four times the speed of sound before it destroyed the target Mirach drone which was heading through the skies above the Outer Hebrides.
Commander Ben Keith, the commanding officer of Portsmouth-based HMS Diamond, said: “An explosion in the sky marked the missile destroying her target, all in all the culmination of another successful week’s work for HMS Diamond.
“I am immensely proud of my team and the work they put in over the past few weeks to make this test firing possible.
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“We have proven once again that the Type 45 destroyer is a world-beating ship when it comes to air defence and this firing gives us the utmost confidence in Diamond and her systems in advance of our deployment later this year.”
The Sea Viper system is a combination of the Sampson radar and the Aster missile system which is capable of tracking aircraft and objects across thousands of miles of airspace.
A Royal Navy spokesman said: “The successful missile firing was the final tick in the box for HMS Diamond’s training package and marks the end of a busy few months for the ship and the men and women on board.
“She will now return to Portsmouth for a final period of preparations before deploying later this year.”
Diamond’s sister ship HMS Daring returned home to Portsmouth last week after a nine-month deployment carrying out security patrols in the Middle East.