The rocket will be carrying a capsule packed with 1,000 pounds of food, water and supplies bound for the ISS, the Los Angeles Times reported. Launch time is set for 8:34 p.m. EDT Sunday from Space Launch Complex 40 at Cape Canaveral.
"I'm still quite nervous about it because it's just our second mission to the station," Elon Musk, SpaceX founder and chief executive, said. "We're hoping that this mission goes as smoothly as the last one."
SpaceX performed a successful demonstration mission in May, showing NASA it could do the job -- and securing the $1.6 billion contract.
SpaceX secured a $440 million contract from NASA in August to develop a capsule to carry astronauts.
Company officials said the upcoming cargo missions will provide SpaceX with necessary flight experience for accomplishing that goal by 2015.