Recently, end-to-end (E2E) models become a competitive alternative to the conventional hybrid automatic speech recognition (ASR) systems. However, they still suffer from speaker mismatch in training and testing condition. In this paper, we use Speech-Transformer (ST) as the study platform to investigate speaker aware training of E2E models. We propose a model called Speaker-Aware Speech-Transformer (SAST), which is a standard ST equipped with a speaker attention module (SAM). The SAM has a static speaker knowledge block (SKB) that is made of i-vectors. At each time step, the encoder output attends to the i-vectors in the block, and generates a weighted combined speaker embedding vector, which helps the model to normalize the speaker variations. The SAST model trained in this way becomes independent of specific training speakers and thus generalizes better to unseen testing speakers. We investigate different factors of SAM. Experimental results on the AISHELL-1 task show that SAST achieves a relative 6.5% CER reduction (CERR) over the speaker-independent (SI) baseline. Moreover, we demonstrate that SAST still works quite well even if the i-vectors in SKB all come from a different data source other than the acoustic training set.