In this paper, a parametric study is conducted to optimize a business jet using supersonic bi-directional (SBiDir) flying wing (FW)aiming at achieving high aerodynamic efficiency and low sonic boom. The SBiDir-FW concept has a symmetric planform about both longitudinal and span axes, allowing the plane to achieve high efficiency at both supersonic and subsonic by rotating by 90 o in flight. With this parametric study, the L/Dp achieves 15 at M=1.6, 16 at M=2.0, whereas the sonic boom remains smooth without N-wave. The smooth peak over pressure value is 0.3 psf at M=1.6, 0.4 psf at M=2.0. It indicates that the conventional N-wave could be replaced by a strong acoustic wave, which generates a much less impulsive force and hence noise. The supersonic aspect ratio of the present configuration is 0.33 and the subsonic aspect ratio is 33, which ensures high performance at both supersonic and subsonic. The study shows that the sharp and long nose configuration with ultra-slender body is favorable to both high aerodynamic efficiency and low sonic boom. The numerical results demonstrate that the SbiDir-FW could be a very promising concept for supersonic flight. Further improvement can still be made by using systematic automated design optimization.