Log parsing, which converts semi-structured logs into structured logs, is the first step for automated log analysis. However, existing parsers are still unsatisfactory in the real world due to new log types in new-coming logs. In practice, the system‘s available logs cannot contain all log types because some latent log types of infrequently activated system states cannot log and systems frequently change to bring new log types. For example, most parsers require preprocessing to extract variables in advance, but preprocessing is based on the operator’s empirical knowledge of available logs and therefore cannot work on new log types. In addition, parser parameters set based on available logs are difficult to generalize to new log types. To support new log types, we propose a variable generation imitation strategy to craft a novel self-supervised log parsing approach, called Log3T. Log3T employs a pretrained transformer encoder-based model to extract log templates and can update parameters at parsing time to adapt to new log types by a modified test-time training. Experimental results on 16 benchmark datasets show that Log3T outperforms the state-of-the-art parsers on parsing accuracy, reaching 0.909. In addition, Log3T can automatically adapt new log types in new-coming logs