A theory of the shock wave structure in a rarefied polyatomic gas is developed on the basis of the recent new approach to extended thermodynamics. We summarize the following points (i) and (ii) based on the previous study on this subject and also show the new point (iii): (i) The theory can explain the change of types of the shock wave structure observed experimentally with the increase of the Mach number from unity; the nearly symmetric shock wave structure (Type A, small Mach number), the asymmetric structure (Type B, moderate Mach number), and the structure composed of thin and thick layers (Type C, large Mach number). (ii) The theoretical prediction of the mass density profile agrees well with experimental data. (iii) The points (i) and (ii) are not strongly affected by the details of the temperature dependence of the bulk viscosity.