We investigated spin transfer torque magnetization precession in a nanoscale pillar spin-valve under external magnetic fields using micromagnetic simulation. The phase diagram of the magnetization precession is calculated and categorized into four states according to their characteristics. Of the four states, the precessional state has two different modes: steady precession mode and substeady precession mode. The different modes originate from the dynamic balance between the spin transfer torque and the Gilbert damping torque. Furthermore, we reported the behavior of the temporal evolutions of magnetization components in steady precession mode at the condition of the applied magnetic field using the orbit projection method and explaining perfectly the magnetization components evolution behavior. In addition, a result of a nonuniform magnetization distribution is observed in the free layer due to the excitation of non-uniform mode.