A Mössbauer spectrometer was built and evaluated using an amplified piezoelectric actuator under feedback control for the Doppler velocity drive. The actuator was driven with a quadratic displacement waveform, giving a linear velocity profile. The optimization of the piezoelectric Doppler drive under feedback control was performed with measurements from a laser Doppler vibrometer. 57Fe Mössbauer spectra of α-iron in transmission geometry show minimal peak distortions. The performance of this piezoelectric Doppler drive makes Mössbauer spectrometry possible in applications requiring small size, mass, and low cost.