Terahertz (THz) technology is a developing and promising candidate for biological imaging, security inspection and communications, due to the low photon energy, the high transparency and the broad band properties of the THz radiation1,2,3. However, a major encountered bottleneck is lack of efficient devices to manipulate the THz wave, especially to modulate the THz wave front. A wave front modulator should allow the optical or electrical control of the spatial transmission (or reflection) of an input THz wave and hence the ability to encode the information in a wave front4. Here we propose a spatial THz modulator (STM) to dynamically control the THz wave front with photo-generated carriers. A computer generated THz hologram is projected onto a silicon wafer by a conventional spatial light modulator (SLM). The corresponding photo-generated carrier spatial distribution will be induced, which forms an amplitude hologram to modulate the wave front of the input THz beam. Some special intensity patterns and vortex beams are generated by using this method. This all-optical controllable STM is structure free, high resolution and broadband. It is expected to be widely used in future THz imaging and communication systems.