Japan's NeXT mission has been approved for the Phase-A in 2007. At present NeXT is in the process of transition to the Phase-B. One of the unique feature of the mission is an imaging spectroscopy in unprecedentedly wide energy region from 0.5 to 80 keV. The X-ray Telescope (XRT) system covers the energy region by means of grazing incidence reflective optics. International collaboration has been formed for the project and design and basic study have been carried out so far. Current baseline specification includes two hard X-ray telescopes which are combined with the Hard X-ray Imager (Si + CdTe pixel or strip) and cover 5 to 80 keV, and two soft X-ray telescopes which cover 0.3 to about 20 keV, one combined with a high resolution X-ray micro-calorimeter and the other with an X-ray CCD. Both of hard and soft X-ray mirrors employ same optical design; tightly-nested, conically-approximated thin-foil Wolter-I optics. The mission requirements for XRT system have been identified as 300 cm2 at 30 keV for the hard X-ray telescope in total and 400 cm2 at 6 keV for the soft X-ray telescope per unit. The requirement on the point spread function is 1.7 arcmin in HPD, as well as the goal being 1.2 arcmin. Based on the current level of technology all the mission requirements are expected to be satisfied.