The optical signal-to-noise ratio (OSNR) and fiber nonlinearity are critical factors in evaluating the performance of high-speed optical fiber communication systems. Recently, several deep learning based methods have been put forward to monitor OSNR of a fiber communication system. In this work, we propose a long short-term memory (LSTM) network based method to simultaneously estimate OSNR and nonlinear noise power caused by fiber nonlinearity. In the training step, LSTM network extracts the essential features in frequency domain of the input signal. Then, with the built model in the training step, the LSTM output the OSNR and nonlinear noise power of the signal under test. The simulation by VPI software is carried on a 5-channel long haul optical transmission system with the launched optical power of -3.0~ + 3.0dBm per channel. The results show that the test error of OSNR is less than 1.0dB with the reference OSNR from 15 to 30dB for QPSK, 16QAM and 64QAM signal. The test error of nonlinear noise power is less than 1.0dB for QPSK and 16QAM signal when the Laser linewidth is 6 KHz and 100 KHz respectively. The proposed method is a promising candidate for nonlinearity-insensitive OSNR and accurate nonlinear noise power estimation in multi-channel long haul optical fiber communication systems.