A laser diode (LD) pumped all-fiber laser with master oscillator power amplification configuration is demonstrated, of which output power is more than 4 kW. The stimulated Raman scattering (SRS) and transverse mode instability (TMI) charateristics of lasers are experimentally studied under different core-diameter gain fibers and different pump wavelengths. In order to mitigate SRS, a large mode area Yb3+ doped fiber with core diameter of 30 μm is selected as gain media. In order to suppress TMI, LD with center wavelength of 915 nm is used as pump source, so the absorption coefficient of the gain fiber is lower at 915 nm, and the bending radius of the gain fiber is reduced to 10 cm to increase the loss of the higher modes. When the seed power is 100 W, the highest pump power is 5.3 kW, the laser power of 4.1 kW is achieved, and the beam quality M2 is 2.2. There are no SRS and TMI effects observed in the output laser.