All-fiber continuous-wave (CW) and passively Q-switched lasers at 1.36 µm (4F3/2 → 4I13/2) by a Nd3+-doped double cladding phosphate fiber are demonstrated for the first time, to the best of our knowledge. To suppress the competitive 0.9 and 1.05 µm emission, the Yb3+ ions are intentionally introduced into the inner cladding of this Nd3+-doped fiber. CW laser at 1.36 µm with a signal-to-noise ratio over 50 dB is realized by using two fiber-type dielectric films as cavity mirrors. A 4.0% CW laser efficiency is obtained when the Nd3+-doped fiber length is 33 mm. The emission at 0.9 and 1.05 µm is well-suppressed, and no parasitic laser is observed. Taking a commercial semiconductor saturable absorber (SA) mirror as the SA, the compact 1.36-µm Q-switched laser is demonstrated, and the repetition rate of output pulses can be tuned from 230 to 522 kHz with a narrowest pulse duration of 152 ns. Our results may provide a promising way to realize 1.3 µm laser oscillation in Nd3+-doped fibers.