Novel high quality factor Q terahertz metamaterials based on asymmetric double split ring resonator as unit cells are reported. When the incident electric field is polarized perpendicular to the ring gaps, the proposed structure simultaneously sustains, the trapped- mode resonance, the mixed- mode resonance and the dipole resonance in different terahertz frequency ranges. The quality factor and center resonance frequency of the resonances can be tuned by changing the gap position and vertical distance between the horizontal metal microstrip lines of the metamaterials unit cells. Numerical simulation results show that the stop band of trapped- mode resonance can reach almost narrow line width of 11.1 GHz and the corresponding quality factor is about 40; the line width of mixed-mode resonance is about 62.4 GHz and the corresponding quality factor is about 16. The proposed high-Q metamaterials have extensive applications in the fields of terahertz research, such as for the high-resolution thin-film sensors, high-performance narrow-band terahertz filters and high frequency modulators.