However, a strong contender for the fastest production car (meaning you could actually *buy* one, though very few people could afford it) around 1960 would be the Ferrari 250 GT SWB Berlinetta Competizione. While exact top speeds weren't precisely measured and publicized like today, its performance suggested a top speed in the 150 mph (240 km/h) range. This is an estimate, and other high-performance cars of the time might have been very close.
It's important to remember that land speed records were being broken regularly, with purpose-built vehicles achieving significantly higher speeds, but those weren't cars you could buy at a dealership.