Multilingual machine translation addresses the task of translating between multiple source and target languages. We propose task-specific attention models, a simple but effective technique for improving the quality of sequence-to-sequence neural multilingual translation. Our approach seeks to retain as much of the parameter sharing generalization of NMT models as possible, while still allowing for language-specific specialization of the attention model to a particular language-pair or task. Our experiments on four languages of the Europarl corpus show that using a target-specific model of attention provides consistent gains in translation quality for all possible translation directions, compared to a model in which all parameters are shared. We observe improved translation quality even in the (extreme) low-resource zero-shot translation directions for which the model never saw explicitly paired parallel data.