We investigate Venus Express observations of magnetic field fluctuations performed systematically in the solar wind at 0.72 Astronomical Units (AU), between 2007 and 2009, during the deep minimum of solar cycle 24. The power spectral densities (PSDs) of the magnetic field components have been computed for time intervals that satisfy the data integrity criteria and have been grouped according to the type of wind, fast and slow, defined for speeds larger and smaller, respectively, than 450 km s-1. The PSDs show higher levels of power for the fast wind than for the slow. The spectral slopes estimated for all PSDs in the frequency range 0.005-0.1 Hz exhibit a normal distribution. The average value of the trace of the spectral matrix is -1.60 for fast solar wind and -1.65 for slow wind. Compared to the corresponding average slopes at 1 AU, the PSDs are shallower at 0.72 AU for slow wind conditions suggesting a steepening of the solar wind spectra between Venus and Earth. No significant time variation trend is observed for the spectral behavior of both the slow and fast wind.