  We calculate the optical conductivity of the CuO double chains of
PrBa$_2$Cu$_4$O$_8$ by the mean-field approximation for the coupled two-chain
Hubbard model around quarter filling. We show that the $\sim$40 meV peak
structure, spectral shape, and small Drude weight observed in experiment are
reproduced well by the present calculation provided that the stripe-type charge
ordering presents. We argue that the observed anomalous optical response may be
due to the presence of stripe-type fluctuations of charge carriers in the CuO
double chains; the fast time scale of the optical measurement should enable one
to detect slowly fluctuating order parameters as virtually a long-range order.
