The success of transfer to improve learning on a target task is highly dependent on the selected source data. Instance-based transfer methods reuse data from the source tasks to augment the training data for the target task. If poorly chosen, this source data may inhibit learning, resulting in negative transfer. The current best performing algorithm for instance-based transfer, TrAdaBoost, performs poorly when given irrelevant source data. We present a novel set-based boosting technique for instance-based transfer. The proposed algorithm, TransferBoost, boosts both individual instances and collective sets of instances from each source task. In effect, TransferBoost boosts each source task, assigning higher weight to those source tasks which show positive transferability to the target task, and then adjusts the weights of the instances within each source task via AdaBoost. The results demonstrate that TransferBoost significantly improves transfer performance over existing instance-based algorithms when given a mix of relevant and irrelevant source data.