Spintronic THz emitters have been widely studied due to their advantages of broadband frequency, high efficiency, and easy fabrication. The spintronic THz signal is proportional to the magnetization of the ferromagnetic (FM) layer and requires an external magnetic field to maximize the THz signal intensity. Recently, a field-free emitter was designed based on a CoFeB/IrMn3 heterostructure via the exchange bias between two films. However, field-free spintronic THz emitters based on a common FM/nonmagnetic metal structure are rare. Here, we fabricate a tunable and field-free THz emitter with giant THz emission modulation ability based on a polyimide/CoFeB/Pt heterostructure. The THz emission can be modulated by changing the curvature radius of the polyimide substrate. After the emitter is forward bent, the THz radiation without an external magnetic field is stronger than in the flat state with a field, which we attribute to in-plane magnetic anisotropy on the FM layer induced by the tensile strain. When we curve the emitter backward, the THz intensity decreases sharply. Moreover, the modulation (ΔS/Smax) of the THz wave from the forward-curved and backward-curved emitter is over 95%, and the device shows good cyclic repeatability. We provide a novel way to design field-free spintronic THz sources, and flexible devices are promising for application in THz devices.