The nonlinear frequency conversion of low-temporal-coherent light holds a variety of applications and has attracted considerable interest. However, its physical mechanism remains relatively unexplored, and the conversion efficiency and bandwidth are extremely insufficient. Here, considering the instantaneous broadband characteristics, we establish a model of second-harmonic generation (SHG) of a low-temporal-coherent pulse and reveal its differences from the coherent conditions. It is found that the second-harmonic spectrum distribution is proportional to the self-convolution of that of a fundamental wave. Because of this, we propose a method for realizing low-temporal-coherent SHG with high efficiency and broad bandwidth, and experimentally demonstrate a conversion efficiency up to 70% with a bandwidth of 3.1 THz (2.9 nm centered at 528 nm). To the best of our knowledge, this is the highest efficiency and broadest bandwidth of low-temporal-coherent SHG to date. Our research opens the door for the study of low-coherent nonlinear optical processes.