Rapid polarization control by an electric field in ferroelectrics is important to realize high-frequency modulation of light, which has potential applications in optical communications. To achieve this, a key strategy is to use an electronic part of ferroelectric polarization. A hydrogen-bonded molecular ferroelectric, croconic acid, is a good candidate, since π-electron polarization within each molecule is theoretically predicted to play a significant role in the ferroelectric-state formation, as well as the proton displacements. Here, we show that a sub-picosecond polarization modulation is possible in croconic acid using a terahertz pulse. The terahertz-pulse-pump second-harmonic-generation-probe and optical-reflectivity-probe spectroscopy reveal that the amplitude of polarization modulation reaches 10% via the electric-field-induced modifications of π-electron wavefunctions. Moreover, the measurement of electric-field-induced changes in the infrared molecular vibrational spectrum elucidates that the contribution of proton displacements to the polarization modulation is negligibly small. These results demonstrate the electronic nature of polarization in hydrogen-bonded molecular ferroelectrics. The ultrafast polarization control via π-electron systems observed in croconic acid is expected to be possible in many other hydrogen-bonded molecular ferroelectrics and utilized for future high-speed optical-modulation devices.