To study the vector spatial solitons in biased two-photon photorefractive crystals, the dynamical evolution equation and the numerical solution of the vector spatial solitons are established. The bright-bright and dark-dark self-coupled vector solitons are predicted by using numerically methods. The dynamical evolutions of the bright-bright self-coupled vector spatial solitons are analyzed numerically. The results indicate that these self-coupled vector solitons can be obtained by using simple numerical integration procedures and their formation are irrespective to the ratio of the intensities of the two optical components. The bright-bright and dark-dark self-coupled vector spatial solitons exist steadily in two-photon photorefractive crystals.