Pump-probe spectroscopic studies were made for a one-dimensional (1D) platinum dimethylglyoxime complex (Pt(dmg)(2)) under excitation in the exciton absorption band using 40 fs pulses. Oscillation with a period of 0.11 ps which is superimposed on the rise of the induced absorption due to the self-trapped exciton (STE) was found for the first time in this system. The oscillation damped with a time constant of 0.1 ps. In a previous work in which 150 fs pulses were used for excitation at various wavelengths, we found that the spectral shape of the induced absorption changed with time in 0.1-0.3 ps after instantaneous rise up. These results were reasonably explained by the formation and the thermalization of the STE. In the framework of the interpretation we have presented, the oscillation superimposed on the induced absorption is considered to originate from the wave packet motion of the STE during thermalization.