in order to construct a six degree of freedom trajectory model in vector form without auxiliary vector, took the derivative of the unit vector that represents the space attitude of the projectile, and put the derivative in the projectile angular momentum equation, which is alternated with cross product, the explicit representation of the kinetic equation for second derivation of the unit vector is obtained, then a six degree of freedom trajectory model without auxiliary vector is established. The components of the vector equations of the model are given, the initial conditions needed to calculate trajectory in the ground coordinate system are discussed. The model provide another way for the six degree of freedom trajectory calculation of the vector for.