We propose an adapter based multi-domain Transformer based language model (LM) for Transformer ASR. The model consists of a big size common LM and small size adapters. The model can perform multi-domain adaptation with only the small size adapters and its related layers. The proposed model can reuse the full fine-tuned LM which is fine-tuned using all layers of an original model. The proposed LM can be expanded to new domains by adding about 2% of parameters for a first domain and 13% parameters for after second domain. The proposed model is also effective in reducing the model maintenance cost because it is possible to omit the costly and time-consuming common LM pre-training process. Using proposed adapter based approach, we observed that a general LM with adapter can outperform a dedicated music domain LM in terms of word error rate (WER).