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With development of high power GaN laser diode (LD) and Bragg gratings writing in fluoride glass and fibers, it's necessary and important to develop a numerical model for visible down conversion Pr 3+-doped fiber (PDF) lasers based on GaN LD and fiber Bragg gratings (FBGs) to optimize its performance for practical use. We propose a numerical model to investigate both steady state and Q-switching dynamics of a visible down conversion PDF lasers. FBGs are placed at both ends of PDF to form a linear cavity. First, the effect of fiber length, boundary reflectivity and the doping concentration on the output power at steady state was obtained and analyzed. The simulation result at steady state qualitatively agree well with previous experimental demonstrations and the FBG based cavity exhibits advantages over conventional PDF system in terms of low threshold and high slope efficiency. After that, by modulating the reflecting spectrum of FBG by using a piezoelectric transducer, Q-switched pulse behavior has been established to illustrate the impact of FBG feedback, pulse repetition frequency (PRF), pumping power, boundary reflectivity and the doping concentration on pulse shape and pulse characteristics. The larger gain factor is found to be the main reason to explain obvious multipeaks, spurious pulses, and considerable energy leakage in red color Q-switching process. Methods to mitigate above mentioned phenomenon have been proposed and demonstrated in this paper.