High efficiency broadband second-harmonic conversion plays an important role in communication, signal processing, spectroscopy and so on. In general, the study of high efficiency broadband second-harmonic conversion focuses on a few of wavelengths. For obtaining tunable high efficiency broadband second-harmonic conversion in quasi-phase matching, the group-velocity and quasi-phase matched condition are analyzed. The temperature effect on high-efficiency broadband second-harmonic conversion in types 0 and Ⅰ quasi-phase matched condition for 5 mol% periodically poled LiNbO3 and periodically poled LiNbO3 is studied. The results show that 15 nm and 341 nm tunable high efficiency broadband second-harmonic conversions are obtained in types 0 and Ⅰ quasi-phase matched conditions for 5 mol% periodically poled LiNbO3; 44 nm and 98 nm tunable high efficiency broadband second-harmonic conversions are obtained in types 0 and Ⅰ quasi-phase matched condition for periodically poled LiNbO3. The range of high efficiency broadband second-harmonic conversion wavelength is expanded.