Through thorough numerical simulations, we investigated the molecular and polarization properties of the vector soliton molecules in an anomalous-dispersion fiber laser for the first time to our best knowledge. The molecular properties of the fast and slow modes of the vector soliton molecule can have different evolution characteristics on the interaction plane. The polarization dynamics of the leading and trailing vector pulses of the vector soliton molecule can have different evolution dynamics on the polarization Poincare sphere. The balance between gain and loss, the coupling between the orthogonal components and the interaction between the leading and trailing pulses result in various physical pictures of the vector soliton molecules in fiber lasers. Our results enrich the vector soliton dynamics in fiber lasers and have potential in optical signal processing and polarization division multiplexing for optical communications.