We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices x and y are connected with probability that asymptotically behaves like |x - y|(-alpha) with alpha > d, where d denotes the dimension of the underlying Euclidean space. More precisely, focus is on the random connection model in which the vertex set is given by the realization of a homogeneous Poisson point process. We show that this random graph exhibits similar properties as classical discrete long-range percolation models studied by Berger (2002) with regard to recurrence and transience of the random walk. Moreover, we address a question which is related to a conjecture by Heydenreich, Hulshof and Jorritsma (2017) for this graph.(c) 2022 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).