This paper proposes and demonstrates an Optical Signal Noise Ratio (OSNR) monitoring scheme using the signal power nonlinear transformation and Deep Neural Networks (DNN). The features of signal after 2th, 4th, and 8th transformation and corresponding Fast Fourier Transformation (FFT) depend on the OSNR of signal. By utilizing the DNN to extract those OSNR depended specific features, the OSNR value can be estimated. Simulation results for 28 Gbaud Polarization Division Multiplexing (PDM)-Quadrature Phase Shift Keying (QPSK), PDM-8 Phase Shift Keying (PSK), PDM-8 Quadrature Amplitude Modulation (QAM) and PDM-16QAM signals show that the OSNR monitoring with mean estimation standard errors of 0.10, 0.09, 0.33 and 0.46 dB in back-to-back case and 0.43, 0.34, 0.66 and 0.79 dB in 2 000, 1 040, 1 040 and 800 km single mode fiber transmission case with input optical power of 4, 4, 3 and 3 dBm, respectively.