Steady-state visual evoked potential (SSVEP) is the brain's response to quickly repetitive visual stimulus with a certain frequency. To increase the information transfer rate (ITR) in SSVEP-based systems, due to the frequency resolution restriction, we are forced to broaden the frequency range, which causes harmonic frequencies to come into the stimulation frequency range. Conventional canonical correlation analysis (CCA) may be associated with error for SSVEP frequency recognition at stimulation frequencies with harmonic relations. The number of harmonics considered to construct reference signals are determined adaptively; for frequencies whose second harmonic exists in the frequency range, two harmonics are used, and for other frequencies, just one harmonic is used. After constructing reference signals and recognizing the frequency corresponding to the maximum value of correlation by CCA, the target frequency is determined after a postprocessing step. Results show that for the 8-s time window length, the average classification accuracy for the adaptive CCA was 84 %, while the corresponding values for the CCA with one harmonic $(N=1)$ and two harmonics $(N=2)$ were 78 % and 74 %, respectively. For 4-s length, this accuracy for the adaptive CCA was 86 %, while it was 78\% for both harmonic selection modes of the standard CCA, $N=1$ and $N=2$. In SSVEP applications with harmonic stimulation frequencies, the adaptive CCA has significantly improved the frequency recognition accuracy in comparison with the popularly standard CCA method. The proposed method can be useful for SSVEP-based BCI systems that use broad ranges of stimulation frequencies with harmonic relation.