By applying the qualitative theory of ordinary differential equations and the Taylor series expansion methods，a class of non-polynomial differential system is analyzed. With the formal series method，the fine focus are analyzed and the center is judged by the principle of symmetry. After the Dulac function，the non-existence of closed orbit is discussed. With the Hopf bifurcation theory，some sufficient conditions for the existence and stability of limit cycles bifurcated from the equilibrium point are also analyzed.