  Using the data from the PCA and HEXTE on board the RXTE satellite, we
investigate the evolution of the 3-200 keV spectra of the peculiar low mass
X-ray binary (LMXB) Cir X-1 along the branches on its hardness-intensity
diagram (HID) from the vertical horizontal branch (VHB), through the horizontal
horizontal branch (HHB) and normal branch (NB), to the flaring branch (FB). We
detect a power-law hard component in the spectra. It is found that the derived
photon indices ($\Gamma$) of the power-law hard component are correlated with
the position on the HID. The power-law component dominates the X-ray emission
of Cir X-1 in the energy band higher than $\sim 20$ keV. The fluxes of the
power-law component are compared with those of the bremsstrahlung component in
the spectra. A possible origin of the power-law hard component is discussed.
