As soft continuum manipulators characterize terrific compliance and maneuverability in narrow unstructured space, low stiffness and limited dexterity are two obvious shortcomings in practical applications. To address the issues, a novel asymmetric coaxial antagonistic tubular robot (CATR) arm with high stiffness has been proposed, where two asymmetrically patterned metal tubes were fixed at the tip end with a shift angle of 180° and axial actuation force at the other end deforms the tube. Delicately designed and optimized steerable section and fully compliant section enable the soft manipulator high dexterity and stiffness. The basic kinetostatics model of a single segment was established on the basis of geometric and statics, and constrained optimization algorithm promotes finding the actuation inputs for a given desired task configuration. In addition, we have specifically built the design theory for the slits patterned on the tube surface, taking both bending angle and stiffness into account. Experiments demonstrate that the proposed robot arm is dexterous and has greater stiffness compared with same-size continuum robots. Furthermore, experiments also showcase the potential in minimally invasive surgery.