Terahertz radiation enables coherent excitation of many fundamental modes, such as molecular rotation [1][2][3] , lattice vibration [4][5][6] and spin precession 7,8 . 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.Searching for high-intensity and tunable narrow-band terahertz (THz) source is motivated by broad scientific and industrial applications, such as the transient state control of materials 1-8 , imaging for security or medical applications 9, 10 , and time-domain spectroscopy 11,12 . Although various THz sources have been developed during the past decades, the high-peak-power narrowband THz source tunable from 1 to 10 THz is still scarce. Electron-accelerator-based THz sources stand out due to their exceptional high peak or average power and wide tunability. However, the peak power decreases rapidly as the radiation frequency increases due to the deteriorating longitudinal coherence 13 . Much work has devoted to overcome this obstacle. The common workaround adopts elaborate arrangements for bunch compression, but it is increasingly difficult to compress the beam even shorter with large beam charge 14 . Another approach commonly used in present THz free electron laser (FEL) is to utilize an optical resonator to accumulate the extracted radiation energy in the low-gain regime, but it requires high repetition rate and multiple separate beamlines to cover the whole 'THz gap' 15 , which leads to a sophisticated design and high maintenance cost.Recently, THz electron bunch trains consisting of multiple equally spaced micro-bunches with

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