Modulation classification plays a key role in decoding cognitive radio, signal identification, menace assessment, spectrum senses, and management, efficient use of available spectrum and increase in the speed of data transfer. Quadrature Amplitude Modulation (QAM) has become an important modulation scheme used in most civilian and military applications. However, algorithms developed so far for these purposes have been limited in classifying higher-order QAM and are also extremely complex. Applications which need to take real-time critical decision based upon modulation types information require that an automatic modulation classification (AMC) algorithm is necessarily simple both in cost and in implementation. This paper, therefore, proposes a novel low-complexity feature-based (FB) method based on evaluating the square modulus of the baseband demodulated received signal, as the only discriminating feature, to classify QAM of any modulation order. Results show, in the presence of combined effects of the carrier phase deviations, timing offset, multipath interference and AWGN, that all QAM modulation types up to 2048-QAM achieve 100% classification accuracy at lower than 10 dB of SNR. The classification algorithm is thus robust in accurately classifying any QAM modulation type even in the presence of combined effects of the common distortions on the received modulated signal.