Future wireless communication systems require in- creasing the data-rate, tremendously, given a limited bandwidth. One solution is to use super high-order constellations in high signal to noise ratio (SNR) regimes. However, in practical systems, these constellations face many issues including hardware impair- ments and system non-linearities. In this paper we focus on the carrier frequency offset (CFO) and investigate its effects on the performance of an orthogonal frequency-division multiplexing (OFDM) system that applies a super quadrature amplitude mod- ulation (super-QAM). Our analysis show that although super- QAM constellations are more sensitive to CFO than low-order QAM constellations, on the other hand, we can take advantage of the high SNR regime that super-QAM constellations are used in and obtain an accurate CFO estimate and consequently reduce error vector magnitude (EVM).