We demonstrate a high-energy, single-frequency, and millisecond (ms) 1336.630-nm amplifier with high beam quality and narrow-linewidth simultaneously based on the Nd3+:(LuxGd1-x)3Ga 5O12 (Nd:LGGG) disordered crystal for the first time. The amplifier system consists of a polarized single-frequency 1336.630-nm LD oscillator, two-stage Raman fiber preamplifier, and four-stage Nd:LGGG main amplifier. The seed laser pulse energy is amplified up to a record high pulse energy of 2.05 J at a repetition rate of 5 Hz and a pulse duration of 1 ms with linewidth as narrower as 0.5 pm. The beam quality factor is ${\rm{M}}^{2}\,= \,1.46$. The wavelength of the single-frequency amplifier can be tuned from 1336.600 to 1336.660 nm. All results indicate that the Nd:LGGG is high performance 1.3-μm laser amplification medium, especially for generating the specific wavelength at 1336.630 nm. Moreover, such laser source with the specific wavelength at 1336.630 nm is promising for the development of a high accuracy 27Al+ ion optical clock.