Recommender systems, tool for predicting users’ potential preferences by computing history data and users’ interests, show an increasing importance in various Internet applications such as online shopping. As a well-known recommendation method, neighbourhood-based collaborative filtering has attracted considerable attentions recently. The risk of revealing users’ private information during the process of filtering has attracted noticeable research interests. Among the current solutions, the probabilistic techniques have shown a powerful privacy preserving effect. The existing methods deploying probabilistic methods are in three categories, one  adds differential privacy noises in the covariance matrix; one  introduces the randomisation in the neighbour selection process; the other  applies differential privacy in both the neighbour selection process and covariance matrix. When facing the k Nearest Neighbour (kNN) attack, all the existing methods provide no data utility guarantee, for the introduction of global randomness. In this paper, to overcome the problem of recommendation accuracy loss, we propose a novel approach, Partitioned Probabilistic Neighbour Selection, to ensure a required prediction accuracy while maintaining high security against the kNN attack. We define the sum of k neighbours’ similarity as the accuracy metric α, the number of user partitions, across which we select the k neighbours, as the security metric β. We generalise the k Nearest Neighbour attack to the βk Nearest Neighbours attack. Differing from the existing approach that selects neighbours across the entire candidate list randomly, our method selects neighbours from each exclusive partition of size k with a decreasing probability. Theoretical and experimental analysis show that to provide an accuracy-assured recommendation, our Partitioned Probabilistic Neighbour Selection method yields a better trade-off between the recommendation accuracy and system security.