A newly designed all-solid step-index Yb-doped aluminosilicate large mode area fiber for achieving high peak power at near diffraction limited beam quality with local adiabatic tapering is presented. The 45µm diameter fiber core and pump cladding consist of active/passively doped aluminosilicate glass produced by powder sinter technology (REPUSIL). A deliberate combination of innovative cladding and core materials was aspired to achieve low processing temperature reducing dopant diffusion during fiber fabrication, tapering and splicing. By developing a short adiabatic taper, robust seed coupling is achieved by using this Yb-doped LMA fiber as final stage of a nanosecond fiber Master Oscillator Power Amplifier (MOPA) system while maintaining near diffraction limited beam quality by preferential excitation of the fundamental mode. After application of a fiber-based endcap, the peak power could be scaled up to 375 kW with high beam quality and a measured M2 value of 1.3~1.7.