Spoken language understanding systems typically consist of a pipeline of automatic speech recognition (ASR) and natural language processing (NLP) modules. Although pre-trained language models (PLMs) have been successful in NLP by training on large corpora of written texts; spoken language with serious ASR errors that change its meaning is difficult to understand. We propose a method for pre-training Japanese LMs robust against ASR errors without using ASR. With the proposed method using written texts, sentences containing pseudo-ASR errors are generated using a pseudo-error dictionary constructed using grapheme-to-phoneme and phoneme-to-grapheme models based on neural networks. Experiments on spoken dialogue summarization showed that the ASR-robust LM pre-trained with the proposed method outperformed the LM pre-trained with standard masked language modeling by 3.17 points on ROUGE-L when fine-tuning with dialogues including ASR errors.