The random fiber laser is established with Yb-doped fiber as gain and single-mode fiber as the random distributed feedback, The maximum output power is 5.1 W and the full width at half maximum (FWHM) is 0.34 nm. The high power laser is realized by employing a main oscillator power amplifier configuration, seeded by the random fiber laser above, whose output power reaches 1102 W with an optical-to-optical efficiency of 78.5%. During the whole amplification process, the laser FWHM is well maintained but the root mean square (RMS) linewidth broadens to 1.24 nm. To suppress the spectral width of the random fiber seed laser, a narrowband fiber Bragg grating is used to filtering the random fiber seed laser, and then to enlarge. The maximum output power reaches 1093 W with FWHM of 0.61 nm and RMS linewidth of 0.92 nm. No amplified spontaneous emission and stimulated Brillouin scattering is observed in the whole amplification process.