Based on Maxwell′s equation, spatially coupling wave equation of self-frequency-doubled (SFD) lasers with quasi-there energy levels was derived by virtue of the rate equation of quasi-there energy levels system and the slowly varying envelop approximation, with the situation that the media end pumped. Characterization of SFD Yb:YAB [YAl3(BO3)4] lasers typically pumped by laser diode (LD) was numerically simulated. The simulation showed that intensity of SFD harmonic increased quadratically with the increase of intensity of fundamental harmonic, while intensity of SFD harmonic and fundamental harmonic decreased sharply with the increase of temperature. Within the effective doubled-frequency length, there are different optimal crystal lengths for fundamental and SFD harmonic output being maximum, respectively. Influence of quality of pumping beam on the fundamental and SFD harmonic output of laser was quantificationally evaluated by means of M2 factor.