This paper presents a Jacobian-based inverse kinematics and open-loop control method for an MRI-guided magnetically-actuated steerable intravascular catheter system. The catheter is directly actuated by magnetic torques generated on a set of current-carrying micro-coils embedded on the catheter tip by the magnetic field of MRI scanner. The Jacobian matrix is derived from a three dimensional kinematic continuum model of the catheter deflection. The inverse kinematics are numerically computed by iteratively applying the inverse of the Jacobian matrix. Experimental evaluation compares a catheter prototype’s desired trajectory to the actual trajectory.