The spacecraft will fly 15 kilometres (50,000 feet) into the air. Previous prototypes have only made short hops of a few hundred metres.
CEO Elon Musk said there was a lot that could go wrong, and gave the rocket a 1-in-3 chance of landing in one piece.
Musk tweeted on Tuesday that SpaceX's enormous Starship spacecraft â€" which the company eventually wants to use to get humans to Mars â€" will undergo its first high altitude test next week. This follows a successful test firing of the current prototype's engines on Tuesday.
