We present the experimental demonstration of a new scheme for the generation of ultrashort pulse trains based on free-electron-laser (FEL) emission from a multipeaked electron energy distribution. Two electron beamlets with energy difference larger than the FEL parameter ρ have been generated by illuminating the cathode with two ps-spaced laser pulses, followed by a rotation of the longitudinal phase space by velocity bunching in the linac. The resulting self-amplified spontaneous emission FEL radiation, measured through frequency-resolved optical gating diagnostics, reveals a double-peaked spectrum and a temporally modulated pulse structure.