Automatic modulation classification (AMC), being an integral part of multi-standard communication systems, allows for the identification of modulation schemes of detected signals. The need for this type of blind modulation classification process can be evidently seen in areas such as interference identification and spectrum management. Consequently, AMC has been widely recognized as a key driving technology for military, security, and civilian applications for decades. A major challenge in AMC is the underlying frequency selectivity of the wireless channel, causing an increase in complexity of the classification process. Motivated by this practical concern, we propose the use of k-nearest neighbor (KNN) classifier based on higher-order of statistics (HOS), which are calculated as features to distinguish between different types of modulation types. The channel is assumed to b multipath frequency-selective and the modulation schemes considered are {2, 4, 8} phase-shift keying (PSK) and {16, 64, 256} quadrature amplitude modulation (QAM). The simulation results confirmed the superiority of this approach over existing methods.