Terahertz radiation enables coherent excitation of many fundamental modes, such as molecular rotation, lattice vibration and spin precession. To excite the transient state of matter far out of equilibrium, high-power and tunable narrow-band THz radiation source has been in great demand for years. However, with such fertile spectrum resources waiting for exploitation, the currently available THz sources cannot satisfy the demands on the tunability and the power level, leaving a large scientific gap scarcely explored. Here, we convert the energy modulation exerted by the nonlinear longitudinal space charge force to density modulation, and for the first time experimentally demonstrate the generation of widely tunable electron bunch trains with modulation frequency adjustable between 1-10 THz. The electron bunch trains can be directly used to produce tunable high-power narrow-band THz radiation fully covering the long-standing ‘THz gap’, which will open up much more possibilities in THz science.