The two-time Olympic gold medallist, riding Horseware Hale Bob, has a 0.4-point advantage over reigning champion Michael Jung on La Biosthetique Sam.
Rosalind Canter is the highest-placed Briton in sixth, with Oliver Townend and Alexander Bragg seventh and eighth.
The Gloucestershire event finishes with show jumping on Sunday.
Ireland's Clare Abbot is in 11th place, while Jonty Evans, who was third after the dressage stage, has dropped to 25th. Australia's Christopher Burton, who led after the dressage on Graf Liberty, is 19th.
1. Ingrid Klimke (Ger) (Horseware Hale Bob) 39.6 pens
2. Michael Jung (Ger) (La Biosthetique Sam FBW) 40
3. Andrew Nicholson (NZ) (Nereo) 40.4
4. Tim Price (NZ) (Xavier Faer) 48.2
5. Mark Todd (NZ) (NZB Campino) 50.4
6. Rosalind Canter (GB) (Allstar B) 54.5
7. Oliver Townend (GB) (ODT Ghareeb) 56.2
8. Alexander Bragg (GB) (Zagreb) 57
9. Mark Todd (NZ) (Leonidas II) 58.1
10. Yoshiaki Oiwa (Jpn) (The Duke of Cavan) 58.2
Germany's Ingrid Klimke leads the Badminton ‎Horse Trials after the cross country phase, as she bids to become the first female winner in a decade.