A vectored mathematical model and stability of a near-space earth observation platform are presented in this paper. First, the reference frames and motion parameters of the platform was defined. Then, a nonlinear six degrees of freedom mathematical model in vector form of the platform was derived based on Newton-Euler principle. Finally, stability of the platform was analyzed by means of Lyapunov stability theory. The results show that the platform is asymptotic stability for the equilibrium. The longitudinal motion and lateral motion of the platform under initial disturbances are both composed of two non-periodic attenuation modes and an oscillation attenuation mode. The fast attenuation mode is related to the angular velocity motion and reflects the process of moments balancing, while the slow attenuation mode is related to the linear velocity and reflects the process of forces balancing.