Aims.We made a seismic study of the young massive β Cephei star HD 203664 with the goal of constraining its interior structure.Methods.Our study is based on a time series of 328 new Geneva 7-colour photometric data of the star spread over 496.8 days.Results.The data confirm the frequency of the dominant mode of the star, which we refined to f_1=6.02885 c d-1. The mode has a large amplitude of 37 mmag in V and is unambiguously identified as a dipole mode (?=2) from its amplitude ratios and non-adiabatic computations. Besides f_1, we discovered two additional new frequencies in the star with amplitudes above 4σ: f_2=6.82902 c d-1 and f_3=4.81543 c d-1, or one of their daily aliases. The amplitudes of these two modes are only between 3 and 4 mmag, which explains why they were not detected before. Their amplitude ratios are too uncertain for mode identification. Conclusions.We show that the observed oscillation spectrum of HD 203664 is compatible with standard stellar models but that we have insufficient information for asteroseismic inferences. Among the large-amplitude β Cephei stars, HD 203664 stands out as the only one rotating at a significant fraction of its critical rotation velocity (~ 40%).