The vibrational spectra of all-trans-1,3,5,7-octatetraene have been studied with nb initio Hartree-Fock (I-IF) and Moller-Plesset second-order perturbation (MP2) calculations. The MP2-predicted spectra are in good agreement with experiment, clearly showing the importance of the electron correlation effect. The basis set dependency is notable. Relative to the experimental data, the mean absolute percentage deviations of vibrational frequencies predicted by HF/DZ, MP2/DZ, and MP2/6-31G* are 12.4%, 3.4%, and 4.4%, respectively. The higher frequencies tend to be overestimated, whereas the lower frequencies do not. Thus, exponential scaling is more suitable than constant scaling. With exponential scaling, the root mean square (rms) frequency deviations of the MP2/DZ and MP2/6-31G* results from the experimental results are 29 and 22 cm(-1) respectively, while with constant scaling the two values are 41 and 26 cm(-1), respectively. Therefore, although the MP2 results with the polarization basis sets seem to predict the frequencies in terms of the mean absolute percentage deviations less accurately than those without the polarization basis sets, the former becomes much more consistent than the latter when the frequencies are scaled. Exponential scaling can be a useful approach in that it turns out to be better than constant scaling which has been commonly used.