Accurate prediction of the motion of a body moving around another one in an unbounded fluid and determi-nation of the hydrodynamic interaction between them are im-portant in the coastal and offshore engineering. For two-dimensional cases, most of the previous studies were focused on the interaction between circular cylinders without considering the non-circular situation. To break through the limitation ofcircular bodies, in the present paper the boundary perturbation method was employed to investigate the motion of a slightly distorted circular cylinder around a circular one. An approximate complex velocity potential in terms of double infinite series expanded at two singular points was derived using the method of continued fractions. The hydrodynamic interaction between two cylinders was computed by solving the dynamical equations of motion. In a relative coordinate system moving with the uniform stream, the kinetic energy of the fluid was expressed as a function of fifteen added masses. Approximate analytical solutions of added masses in the series form were obtained and applied to determine the trajectories of the slightly distorted circular cylinder around a fixed circular one. Numerical results show that the presence of the circular cylinder affects the planar motion of the slightly distorted cirular cylinder and the initial configuration of the slightly distorted circular cylinder has a decisive influence on the development of its rotational motion.