Newly promoted group managing director Neil Fitzsimmons said that Redrow could reach the target with existing resources but did not set a timescale.
Fitzsimmons said: "We are planning the business looking at organic growth. We made 4031 completions last year but have the capacity to go up to 6000."
Nearly half the completions this year came from the northern division, which finished 1982 homes compared with 1888 in the previous 12 months.
Fitzsimmons said that growth would be driven partly by the company's steel frame business.
Last July Redrow signed a joint venture with steel manufacturer Corus and claimed that it would cut build time by 30%.
The joint venture, called Framing Solutions, has produced more than 500 units in the past year but Fitzsimmons said that by 2006 it could have an output of 2000 units. Not all of these would be for Redrow; some frames would be sold to other housebuilders.
Fitzsimmons made the comments after his promotion was announced with the group's annual results on Tuesday.
The housebuilder has joined the likes of Bellway and Bovis Homes in the £100m pre-tax profit club. In the 12 months to June, Redrow made a profit of £106.1m – an increase of 24.7% on the previous year. Turnover rose 6% to £607.9m.
Chairman Robert Jones said: "Redrow has had a record year, delivering further growth, with profit before tax exceeding the milestone of £100m. Against a background of a stable housing market, a continuing undersupply of new homes and pent-up aspiration to home ownership, I remain confident that Redrow will go from strength to strength."
Jones said that he expected consolidation in the sector to continue but laughed off rumours that Redrow might merge or be taken over by a rival. He added that the company itself has not ruled out the possibility of acquisitions but was not actively pursuing any smaller housebuilder.
Redrow also announced several other board changes. Rhiannon Walker has stepped down as company secretary after 16 years and has been succeeded by Graham Cope. Non-executive director Bob Williams will also stand down at Redrow's annual general meeting on 5 November. It was also announced that David Arnold has been made group finance director.