Brain tumor segmentation from Magnetic Resonance Images (MRIs) is an important task to measure tumor responses to treatments. However, automatic segmentation is very challenging. This paper presents an automatic brain tumor segmentation method based on a Normalized Gaussian Bayesian classification and a new 3D Fluid Vector Flow (FVF) algorithm. In our method, a Normalized Gaussian Mixture Model (NGMM) is proposed and used to model the healthy brain tissues. Gaussian Bayesian Classifier is exploited to acquire a Gaussian Bayesian Brain Map (GBBM) from the test brain MR images. GBBM is further processed to initialize the 3D FVF algorithm, which segments the brain tumor. This algorithm has two major contributions. First, we present a NGMM to model healthy brains. Second, we extend our 2D FVF algorithm to 3D space and use it for brain tumor segmentation. The proposed method is validated on a publicly available dataset.