Based on the simplified model of fiber laser,the transmission characteristics of bright-dark soliton pair in fiber laser are studied numerically by the split-step Fourier method. The results show that the stable existence of the bright-dark soliton pair is related to the group velocity dispersion, and the bright-dark soliton pair can maintain the stable transmission in the zero dispersion region. At the same time, the bright-dark soliton pair is influenced by the small signal gain coefficient, saturated energy, initial pulse width, and polarization angle in fiber laser. The larger the small signal gain coefficient or the saturation energy,the peak intensity of the bright-dark soliton pair is greater with the width narrower. When the peak intensity increases to a certain degree, the bright-dark soliton pair is split. The polarization controller can control the output of the bright-dark soliton pair. These results can provide some theoretical basis for the research on the generation of signal sources of bright-dark soliton pair in fiber laser.