End-to-end (E2E) automatic speech recognition (ASR) systems directly map acoustics to words using a unified model. Previous works mostly focus on E2E training a single model which integrates acoustic and language model into a whole. Although E2E training benefits from sequence modeling and simplified decoding pipelines, large amount of transcribed acoustic data is usually required, and traditional acoustic and language modelling techniques cannot be utilized. In this paper, a novel modular training framework of E2E ASR is proposed to separately train neural acoustic and language models during training stage, while still performing end-to-end inference in decoding stage. Here, an acoustics-to-phoneme model (A2P) and a phoneme-to-word model (P2W) are trained using acoustic data and text data respectively. A phone synchronous decoding (PSD) module is inserted between A2P and P2W to reduce sequence lengths without precision loss. Finally, modules are integrated into an acousticsto-word model (A2W) and jointly optimized using acoustic data to retain the advantage of sequence modeling. Experiments on a 300- hour Switchboard task show significant improvement over the direct A2W model. The efficiency in both training and decoding also benefits from the proposed method.