This paper researches Fock state space structure and supersymmetry mechanics of parasystem consisting of one degree of freedom of paraboson and one degree of freedom parafermion in the case of the same order p.It is shown that except for the four extreme special states,there is an intrinsic double-degeneracy in the state space structure of a parasystem.Moreover,it is also discovered that the parasystem possesses a hidden intrinsic supersymmetry in addition to the dynamic supersymmetry,and the intrinsic supersymmetry plays a key role in the exact supersymmetry of a parasystem.