The refinery crude unit was earlier shut down due to a fire experienced on 28 July 2010.
The company expects to resume throughput and production later in the week.
The accelerated maintenance on the naphtha reformer and diesel hydrotreater have also been completed, and these units will restart normal operations along with the crude unit.
Frontier operates a 135,000bpd refinery located in El Dorado, Kansas, and a 52,000bpd refinery located in Cheyenne, Wyoming, and markets its refined products principally along the eastern slope of the Rocky Mountains and in other neighboring plains states.