In this study, a novel method of phase constrained canonical correlation analysis (p-CCA) is presented for classifying steady-state visual evoked potentials (SSVEPs) using multichannel electroencephalography (EEG) signals. p-CCA is employed to improve the performance of the SSVEP-based brain-computer interface (BCI) system using standard CCA. SSVEP response phases are estimated based on the physiologically meaningful apparent latency and are added as a reliable constraint into standard CCA. The results of EEG experiments involving 10 subjects demonstrate that p-CCA consistently outperforms standard CCA in classification accuracy. The improvement is up to 6.8% using 1-4 s data segments. The results indicate that the reliable measurement of phase information is of importance in SSVEP-based BCIs.