We demonstrate an electrically tunable terahertz (THz) modulator based on the single channel AlGaN/GaN high electrons mobility transistor (HEMT). HEMT integrated in the modulator structures is used to change the conductance of the modulator by the applied gate voltage V-g. Under the radiation of THz electromagnetic wave, the change of THz transmissivity through the modulator can be controlled by V-g. The THz modulation depth shows about 33% at the working frequency of 0.835 THz under the DC voltage V-g=-3 V. When the AC modulation voltage V-g is applied on the modulator, the THz modulation depth is about 23% at the modulation frequency of 20 MHz. The good agreement between experiments and finite difference time domain simulation indicates that the good performance of electrically tunable THz modulator can also be realized by using the single channel AlGaN/GaN heterostructure.