The spectrum of atomic vanadium was recorded using high-resolution Fourier transform spectroscopy with optical bandpass filters in the wavelength range from 360 to 500 nm. Vanadium atoms are produced and excited in a hollow-cathode discharge. The main focus lies on the determination of the magnetic dipole hyperfine constants A of the lowest multiplet of odd parity, the (6)G of the configuration 3d(3)4s4p, the hyperfine structure (HFS) of which was unknown to date. The HFS of the lines, connecting this multiplet with the multiplets 3d(3)4s5s F-6, 3d(3)4s4d H-6 and 3d(3)4s4d (6)G, was observed and analysed. New results are presented for all six levels belonging to 3d(3)4s4p (6)G as well as for seven high-lying levels belonging to 3d(3)4s4d H-6 and 3d(3)4s4d (6)G. The experimental results for the lowest multiplet of odd parity are compared with calculated magnetic dipole hyperfine constants which were estimated using the effective-operator formalism in the pure LS coupling case.