The experimental emissions-free aircraft is expected to take about 12 hours to complete the journey to Brussels Airport, the team said.
The dragon fly-like single seater, piloted by co-founder Andre Borschberg, lifted off gently in clear blue skies from Payerne airbase, in western Switzerland, at 8:40 am (0640 GMT) after being delayed by early morning mist, an AFP photographer said.
Solar Impulse HB-SIA, which has the wingspan of a large airliner but weighs no more than a saloon car, made history in July 2010 as the first manned plane to fly around the clock and through the night on the sun's energy.
It holds a record for the longest flight by a manned solar-powered aeroplane after staying aloft for 26 hours, 10 minutes and 19 seconds above Switzerland, also setting a record for altitude by flying at 9,235 metres (30,298 feet).
The high-tech plane has since flown several times, notably between the Geneva and Zurich airports, but the hop to Brussels through crowded airspace is regarded as a new challenge.
"Flying an aircraft like Solar Impulse through European airspace to land at an international airport is an incredible challenge for all of us, and success depends on the support we receive from all the authorities concerned," said Borschberg, who also piloted July's flight.
Images and some control details were being streamed live on the Internet, but pictures were briefly interrupted after it took off and headed north because of a surge in connections, according to a note on the Solar Impulse website.
The aircraft HB-SIA relies on 12,000 solar cells on its 64-metre wings to charge the batteries that provide the energy for its four 10-horsepower electric propellor engines.
The showcase for green technology will go on display at Brussels airport until May 29 before flying on to the international air show at Le Bourget in Paris from June 20 to 26.
"This time, we have a real airplane -- flying -- proof that new technologies can reduce our dependence on fossil energy," said Bertrand Piccard, joint founder and president of the Solar Impulse project.
The Solar Impulse team is planning to fly even further, including possible transamerican, transatlantic and round-the-world flights -- in stages -- in 2013 and 2014 using a slightly larger aircraft.
Piccard, himself the first man along with Briton Brian Jones to fly nonstop around the world in a balloon, comes from a dynasty of pioneers.
His grandfather Auguste Piccard twice beat the record for reaching the highest altitude in a balloon, in 1931-32.
His late father Jacques Piccard was a deep sea explorer, who holds the record for travelling to the deepest point underwater, 10,916 metres (35,813 feet) below sea level in the Marianas Trench in the Pacific.