Abstract: The binormal surfaces were studied by using moving frame, curve theory and its properties, etc. The binormal surfaces characteristics of some special curves were obtained, and, in particular, some characteristic curves on these surfaces were determined. Based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the binormal surfaces of curves and the curves with constant Gaussian curvature were obtained as well as the special properties of the center locus of torsion on the binormal surfaces of such curves. Mannheim partner curves, as the special space curves, have good geometric and algebraic properties. The binormal surfaces of Mannheim partner curves were also studied, and the results showed that the ratio of two principal curvatures on the Mannheim curves was-1. The results also indicated that Mannheim curves were the minimal loci of the binormal surfaces of Mannheim partner curves.