The spacecraft lifted off from Wallops Island, Virginia at 12:52 pm (local time) aboard a gleaming white Antares rocket.
A NASA commentator described the launch as a "flawless 10-minute ride to orbit."
The spacecraft is packed with 1,657 kilograms of food, equipment, science experiments and tools, Orbital Sciences Corp. Said.
The launch marks the second of eight missions the company has contracted with NASA, and is the third journey by Orbital to the International Space Station after a successful demonstration trip last year.
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A new flock of satellites, food and supplies for the crew, experiments for growing arugula in space, and a pump for the Japanese module to replace one that failed are among the items on board the spacecraft.
The Cygnus should arrive at the orbiting outpost on July 16.
American astronaut Steve Swanson and crewmates aboard the station will reach out with the ISS's robotic arm to grab the cargo ship, aided by NASA mission control in Houston, Texas.
Orbital Sciences and SpaceX are the two private US companies that have won major contracts with NASA for multiple missions to carry supplies to the International Space Station.
Orbital's deal is worth USD 1.9 billion and SpaceX's contract is USD 1.6 billion.
Orbital's cargo ships burn up on reentry into Earth's atmosphere, unlike SpaceX's Dragon spacecraft, which makes an intact splash landing in the ocean.