In high power fiber amplifier which uses large mode area (LMA) fiber, the high-order modes(HOM) appear with the increase of laser output power, and the beam quality degrades severely. The influence of fiber bending on thresholds of HOM is studied in experiments based on the fiber bending loss theory. A ytterbium-doped all- fiber narrow- linewidth and high power master- oscillator power amplifier (MOPA) system is built. Novel watering cooling plates of different sizes are designed and used in the main amplifier stage. By using these plates, a series of optimizing experiments are done with the LMA fiber bending at different radii. The threshold of highorder modes are raised successfully and kW-class nearly single mode laser output is obtained. The beam quality factor (M2) is about 1.4 at 1.31 kW.