Swiss pilot Andre Borschberg, 62, left the ground in Nagoya, in central Japan, around 3:00 a.m local time (1800 GMT), five days after weather problems forced the organisers to cancel an earlier attempt to reach Hawaii.
"It took off at 3 o'clock and 4 minutes (am at local time)," spokeswoman Elke Neumann said.
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She added that the weather looked good for now but could still change.
The journey to Hawaii is 7900km (4900 miles) and is expected to last at least five days and five nights.
With nowhere to land after leaving Japan, it is considered the most risky leg so far.
The plane has been stranded in Japan for more than three weeks and had to postpone a planned take off last week due to bad weather over the Pacific Ocean.
In an interview published last Thursday, one of its two pilots, Bertrand Piccard, said it must cross the Pacific within a few weeks or it could remain stuck in Japan for a year.
By early August, the days will become too short for the solar-driven plane to cross the Pacific, and subsequently the Atlantic Ocean safely, he told the Tribune de Geneve daily.
Solar Impulse 2 set off from Abu Dhabi earlier this year in a multi-leg attempt to get all the way around the world without a single drop of fuel.
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