The number of selectable targets is one of the main factors that affect the performance of a brain-computer interface (BCI). Most existing code modulated visual evoked potential (c-VEP) based BCIs use a single pseudorandom binary sequence and its circularly shifting sequences to modulate different stimulus targets, making the number of selectable targets limited by the length of modulation codes. This paper proposes a novel paradigm for c-VEP BCIs, which divides the stimulus targets into four target groups and each group of targets are modulated by a unique pseudorandom binary code and its circularly shifting codes. Based on the paradigm, a four-group c-VEP BCI with a total of 64 stimulus targets was developed and eight subjects were recruited to participate in the BCI experiment. Based on the experimental data, the characteristics of the c-VEP BCI were explored by the analyses of auto- and cross-correlation, frequency spectrum, signal to noise ratio and correlation coefficient. On the basis, single-trial data with the length of one stimulus cycle were classified and the attended target was recognized. The averaged classification accuracy across subjects was 88.36% and the corresponding information transfer rate was as high as 184.6 bit/min. These results suggested that the c-VEP BCI paradigm is both feasible and effective, and provides a new solution for BCI study to substantially increase the number of available targets.