The A1 Sigma +-X1 Sigma + system of KRb was excited using a titanium-doped sapphire laser. Fluorescence spectra were recorded on a Bomem Fourier transform spectrometer, using an apodised linewidth of 0.045 cm-1. Rotational and vibrational constants are reported for the ground state, X1 Sigma +, covering the range 0<or=v<or=44 and J<141.