The use of brain-wave patterns extracted from electroencephalography (EEG) brain signals for person verification has been investigated recently. The challenge is that the EEG signals are noisy due to low conductivity of the human skull and the EEG data have unknown distribution. We propose a multi-sphere support vector data description (MSSVDD) method to reduce noise and to provide a mixture of hyperspheres that can describe the EEG data distribution. We also propose a MSSVDD universal background model (UBM) to model impostors in person verification. Experimental results show that our proposed methods achieved lower verification error rates than other verification methods.