In this paper, we show that the SO(3) chiral field can be regard as the normal Vector field over the pseudo-spherical surface, and thus obtain the correspondence between chiral field and sine-Gordon system, as well as the geometrical interpretation of chiral field. By means of the dual symmetry between chiral field and the pseudo-spherical surface, we are able to connect chiral field with s-G system, and express Backlund transformation, Riccati equation in the gauge invariant representations of the related properties of the same dynamical system in different frames.