The space company had an introductory price of $135, which rose to $150 when trading in the stock began just before 6 p.m.
The stock then continued to climb and peaked at around $175, but fell back slightly and closed at $161.10 after the first day of trading.
The initial public offering of SpaceX - part of Tesla founder Elon Musk's empire - is the largest of all time.
Together with his stake in Tesla, the listing of SpaceX means that Musk is now the world's first trillionaire (one trillion dollars), CNBC reports.
