We shall construct complex contact similarity manifolds. Among them there exists a complex contact infranilmanifold L/Γ which is a holomorphic torus fiber space over a quaternionic euclidean orbifold. Specifically taking a connected sum of L/Γ with the complex projective space CP 2n+1 , we prove that the connected sum admits a complex contact structure. Our examples of complex contact manifolds are different from those known previously as complex Boothby-Wang fibration (Foreman, 2000) or the twistor fibration (Salamon, 1989) .