Given a learning task for a data set, learning it together with related tasks (data sets) can improve performance. Gaussian process models have been applied to such multi-task learning scenarios, based on joint priors for functions underlying the tasks. In previous Gaussian process approaches, all tasks have been assumed to be of equal importance, whereas in transfer learning the goal is asymmetric: to enhance performance on a target task given all other tasks. In both settings, transfer learning and joint modelling, negative transfer is a key problem: performance may actually decrease if the tasks are not related closely enough. In this paper, we propose a Gaussian process model for the asymmetric setting, which learns to “explain away” non-related variation in the additional tasks, in order to focus on improving performance on the target task. In experiments, our model improves performance compared to single-task learning, symmetric multi-task learning using hierarchical Dirichlet processes, and transfer learning based on predictive structure learning.