In recent years, a great deal of attention has been paid to the Transformer network for speech recognition tasks due to its excellent model performance. However, the Transformer network always involves heavy computation and large number of parameters, causing serious deployment problems in devices with limited computation sources or storage memory. In this paper, a new lightweight model called Sim-T has been proposed to expand the generality of the Transformer model. Under the help of the newly developed multiplexing technique, the Sim-T can efficiently compress the model with negligible sacrifice on its performance. To be more precise, the proposed technique includes two parts, that are, module weight multiplexing and attention score multiplexing. Moreover, a novel decoder structure has been proposed to facilitate the attention score multiplexing. Extensive experiments have been conducted to validate the effectiveness of Sim-T. In Aishell-1 dataset, when the proposed Sim-T is 48% parameter less than the baseline Transformer, 0.4% CER improvement can be obtained. Alternatively, 69% parameter reduction can be achieved if the Sim-T gives the same performance as the baseline Transformer. With regard to the HKUST and WSJ eval92 datasets, CER and WER will be improved by 0.3% and 0.2%, respectively, when parameters in Sim-T are 40% less than the baseline Transformer.