A new approach for dual-mode (namely broadband mode and narrowband mode) terahertz (THz) pulses generation in a single lithium niobate (LN) crystal excited by spatially shaped tilted-pulse-front femtosecond (fs) laser pulse was proposed and experimentally demonstrated. The two THz emission modes are generated simultaneously while spatially separated. Both central frequency and bandwidth of narrowband THz emission is controllable by in situ tuning the spatial modulation period and beam size of the fs-laser, and the broadband (0.1-1.5 THz) THz emission keeps almost unchanged while tuning the narrowband emission. Further optimization achieves the narrowband THz emission with energy spectral density up to 0.27 μJ/THz and with bandwidth narrowly down to 23 GHz. Such dual-mode THz source is useful for nonlinear THz optics, such as selected resonant THz excitation with broadband THz probe spectroscopy of crystalline matters.