In this paper, the optimal performance of optical second-order polarization mode dispersion (PMD) compensation has been investigated theoretically in terms of minimization of the root-mean-square (RMS) pulse broadening. The optimal compensation vector in feedforward-type second-order PMD compensation has been derived, and the RMS pulse broadening factor after the optimal second-order PMD compensation has been analytically calculated. The calculated result has been compared with the previously reported simulation result where numerically optimized feedback scheme was adopted. They are in good agreement, which verifies the validity of the derivation. The investigation in this work will form the basis for the implementation of the feed-forward-type second-order PMD compensation.