A modulated grating Y-branch laser (MGY) is an ideal light source for fiber grating demodulation system.At present,there are few modeling studies on its tuning characteristics.In order to study the tuning characteristics of MGY,this paper extended the transmission line laser model (TLLM) to simulate MGY.The Y-type laser with analog modulated grating is studied by combining the TLLM,transmission matrix method (TMM) and digital filtering method.In the combined model,we use the TMM method based on time domain for the gain region and phase region.Firstly,the TMM based on frequency domain is used for the left and right modulated grating (LMG/RMG) regions,and then the inverse Fourier transform is used as the time domain model.The output current characteristic curve and static tuning characteristic of the MGY are simulated successfully,which is similar to the published experimental results.This comprehensive model can be used to study the transient response and laser spectra of devices that are difficult to obtain using frequency-domain models.