A noncontact directive sensor for detecting an angle of a line normal to a curved surface made of ferromagnetic material has been developed. This senser can be used for measuring the accuracy of 3D-shapes, such as molds and dies on machine tools, and autonomous tracing of industrial robots. This sensor has a permanent magnet which can be tilted in any direction and four Hall elements for detecting the angle. The angle is computed from Hall voltages originating from the magnetic flux density. The distance between the curved surface and one magnet end can be detected by means of Hall elements. The experimental results showed that the resolution of the angle was 0.02 degrees, the mean of measurement error was 0.2 degrees, the standard deviation of measurement error was 0.15 degrees and the resolution of distance was 0.5μm around 1mm.