Broadband quasi-phase-matching (QPM) is widely used in many fields, such as multi-wavelength and ultrashort pulse frequency doubling. The conditions of QPM and group velocity matching in lithium niobate crystal are analyzed. The optimized structure of aperiodically poled lithium niobate (APPLN) crystal is designed by genetic algorithm. Also, we present a method of optimizing the APPLN crystal second-harmonic generation (SHG) bandwidth by appropriately adjusting the position and quantity of the fundamental wavelengths. The results show that for QPM of type 0 (e+e→e) near the group velocity matching points, the SHG bandwidth in periodically poled lithium niobate (PPLN) crystal is about 167 nm, while the maximum SHG bandwidth in APPLN is up to 440 nm, and the bandwidth increases by 273 nm. For QPM of type I (o+o→e) near the group velocity matching points, the SHG bandwidth in PPLN is about 59 nm, while the maximum SHG bandwidth in APPLN is up to 153 nm, and the bandwidth increases by 94 nm.