Synaptic plasticity provides the basis for learning mechanism in neural network. Anti-spike-timing-dependent plasticity (anti-STDP) learning mechanism is implemented by the nonlinear polarization rotation (NPR) and cross-gain modulation (XGM) based on single semiconductor optical amplifier (SOA). By adjusting the drive current of SOA, the weight and height of long-term potentiation (LTP) and long-term depression (LTD) windows can be adjusted to better mimic the neural network. The anti-STDP learning curves measured by the experiment closely resemble the learning curves measured by the biological system. Using the proposed anti-STDP optical circuit, the time window of anti-STDP learning curves is about several hundred picoseconds, which is 108 times faster than the speed of STDP learning mechanism in human brain. Since the proposed anti-STDP optical circuit is simple, and SOA can be integrated with some other devices easily, it can be used to realize large-scale and ultrafast neuromorphic computing systems.