A single-frequency quasi-continuous-wave partially end-pumped slab (Innoslab) laser amplifier at 1319 nm was demonstrated. The 3-W single-frequency all-fiber seed laser was amplified to a maximum average power of 80.1 W and the power stability was 0.52% in 10 minutes. The corresponding optical-optical efficiency was 16.1% under absorbed pump power of 478 W. The output pulse width was 131 µs at the repetition of 500 Hz. The beam quality factors of M2 were 1.3 in both the vertical and horizontal directions. To the best of our knowledge, this is the first report on single-frequency Nd:YAG Innoslab amplifier at 1319 nm with such high output power and efficiency.