Depends on the target grade.
For a 4.0 Ielts, I don't think it takes more than 2 months. Another half a years, from 4.0 to 6.0. Above 6.0 may forever be a dream if you don't really beat your ass learning. Though within 2 months, I went from 4.5 to 6.5; and went from 6.5 to 8.0 without...