We address the well-known distance constrained capacitated vehicle routing problem (DCVRP) by considering Euclidean distances, in which the aim is to determine the routes to be performed to fulfil the demand of the customers by using a homogeneous fleet. The objective is to minimise the sum of the variable costs associated with the distance travelled by the performed routes. In this paper, we propose a metaheuristic algorithm based on a probabilistic granular tabu search (pGTS) by considering different neighbourhoods. In particular, the proposed algorithm selects a neighbourhood by using a probabilistic discrete function, which is modified dynamically during the search by favouring the moves that have improved the best solution found so far. A shaking procedure is applied whenever the best solution found so far is not improved for a given number of iterations. Computational experiments on benchmark instances taken from the literature show that the proposed approach is able to obtain high quality solutions, within short computing times.