To efficiently train quality estimation of text simplification on a small-scale labeled corpus, we train sentence difficulty estimation prior to fine-tuning the pre-trained language models. Our proposed method improves the quality estimation of text simplification in the framework of transfer fine-tuning, in which pre-trained language models can improve the performance of the target task by additional training on the relevant task prior to fine-tuning. Since the labeled corpus for quality estimation of text simplification is small (600 sentence pairs), an efficient training method is desired. Therefore, we propose a training method for pseudo quality estimation that does not require labels for quality estimation. As a relevant task for quality estimation of text simplification, we train the estimation of sentence difficulty. This is a binary classification task that identifies which sentence is simpler using an existing parallel corpus for text simplification. Experimental results on quality estimation of English text simplification showed that not only the quality estimation performance on simplicity that was trained, but also the quality estimation performance on fluency and meaning preservation could be improved in some cases.