The first flight landed at 12.15 pm at Bagdogra from DumDum and around 1.20 pm flew off to Kathmandu.
It returned back to Bagdogra at 6 pm, a Spicejet spokesperson said in Bagdogra.
This flight will operate three times a week - on Mondays, Wednesdays and Fridays.
With the introduction of this flight, SpiceJet will become the first Indian airline to operate international flights between Kathmandu and Bagdogra.
"This is our first international flight from the state of West Bengal to Kathmandu. We believe this flight will not only facilitate tourism, but also be important for the growth of trade between the two neighbouring nations," Kaneswaran Avili, chief commercial officer of SpiceJet Ltd, said.