Attention-based encoder-decoder (AED) models have shown impressive performance in ASR. However, most existing AED methods neglect to simultaneously leverage both acoustic and semantic features in decoder, which is crucial for generating more accurate and informative semantic states. In this paper, we propose an Acoustic and Semantic Cooperative Decoder (ASCD) for ASR. In particular, unlike vanilla decoders that process acoustic and semantic features in two separate stages, ASCD integrates them cooperatively. To prevent information leakage during training, we design a Causal Multimodal Mask. Moreover, a variant Semi-ASCD is proposed to balance accuracy and computational cost. Our proposal is evaluated on the publicly available AISHELL-1 and aidatatang_200zh datasets using Transformer, Conformer, and Branchformer as encoders, respectively. The experimental results show that ASCD significantly improves the performance by leveraging both the acoustic and semantic information cooperatively.