Shell has for years been seeking permission to drill in the Beaufort and Chukchi seas, but faces opposition from environmental groups that fear the impact of drilling in the ecosystem that's home to endangered and fragile species.
The company's multibillion-dollar quest to drill in the harsh Arctic seas is frequently cited by Republicans that allege the White House has placed undue restrictions on U.S. energy development.
The GOP-controlled House recently passed legislation aimed at speeding up permitting and easing some air-pollution requirements.
Odum said the company has filed two exploration plans with the Interior Department to drill as many as 10 wells over two years.
The company is vowing to drill with robust safety and spill-response plans.
"It’s relatively simple drilling; it’s a very, very sensitive environment," Odum said.