We propose a bi-directional gated recurrent unit neural network based nonlinear equalizer (bi-GRU NLE) for coherent optical communication systems. The performance of bi-GRU NLE has been experimentally demonstrated in a 120 Gb/s 64-quadrature amplitude modulation (64-QAM) coherent optical communication system with a transmission distance of 375 km. Experimental results show that the proposed bi-GRU NLE can significantly mitigate nonlinear distortions. The Q-factors can exceed the hard-decision forward error correction (HD-FEC) limit of 8.52 dB with the aid of bi-GRU NLE, when the launched optical power is in the range of -3 dBm to 3 dBm. In addition, when the launched optical power is in the range of 0 dBm to 2 dBm, the Q-factor performances of the bi-GRU NLE and bi-directional long short-term memory neural network based nonlinear equalizer (bi-LSTM NLE) are similar, while the number of parameters of bi-GRU NLE is about 20.2% less than that of bi-LSTM NLE, the average training time of bi-GRU NLE is shorter than that of bi-LSTM NLE, the number of multiplications required for the bi-GRU NLE to equalize per symbol is about 24.5% less than that for bi-LSTM NLE.