It has been observed that when the multi-frequency Raman scattering process is pumped by two frequency chirped pulses in the transient regime, the anti-Stokes orders are spectrally broadened on the lower-frequency side, causing each of the orders to have a broader spectrum with double-peak pattern. In this article, we employ frequency-resolved optical gating to study the spectral shift of the first anti-Stokes Raman order. A double-pulse model is introduced to determine the electric field of the anti-Stokes orders from the experimental FROG spectrogram. With the help from the double-pulse model, we demonstrate that the double-peaked spectrum comes from linear Raman scattering between manifolds in the two-photon dressed states.