Blind modulation format identification (MFI) is essential in an elastic optical network (EON) due to unknown modulation format of the received signals. We propose an MFI method for square and non-square quadrature amplitude modulation (QAM) signals, quadrature phase-shift keying (QPSK), 8-QAM, 16-QAM, 32-QAM, 64-QAM, 128-QAM, 256-QAM, 512-QAM, 1024-QAM, and 2048-QAM. We identified these modulation formats by using two identification factors such as the amplitude variance and the optical signal-to-noise ratio (OSNR) of the received signal. The simulation results based on a look-up-table (LUT) and a neural network, respectively, show that the modulation format of the received signals can be identified correctly in the OSNR range of a bit error rate (BER) for communication, better than 10−2. We also investigate effects of both ONSR measurement errors and residual chromatic dispersion (CD) on the MFI performance.