In this paper, Er/Yb co-doped fiber amplifiers (EYDFAs) with an Yb-band fiber Bragg grating (FBG) at the pump end to improve the performance of the amplifier is systematically studied. The influence of the reflectivity and center wavelength of the FBG along with the gain-fiber length on the performance of an EYDFA are numericallyanalyzed. The results show that the wavelength of the FBG has critical influence on the efficiency of the EYDFA, whereas the requirement to its reflectivity is relaxed. It is an effective and promising way to improve the efficiency of a high-power pumped EYDFA by introducing a suitable Yb-band FBG at the pump end. Based on the analysis of the underlying principles, suggestions for the practical design and possible further improvement strategies are also proposed.61107035 and 61378043, the National Key Scientific Instrument and Equipment Development Project of China under grant 2013YQ03091502, and the National Basic Research Program of China (973 Program) under grant 2014CB340104.