Software logs record system activities, aiding maintainers in identifying the underlying causes for failures and enabling prompt mitigation actions. However, maintainers need to inspect a large volume of daily logs to identify the anomalous logs that reveal failure details for further diagnosis. Thus, how to automatically distinguish these anomalous logs from normal logs becomes a critical problem. Existing approaches alleviate the burden on software maintainers, but they are built upon an improper yet critical assumption: logging statements in the software remain unchanged. While software keeps evolving, our empirical study finds that evolving software brings three challenges: log parsing errors, evolving log events, and unstable log sequences. In this paper, we propose a novel unsupervised approach named Evolving Log analyzer (EvLog) to mitigate these challenges. We first build a multi-level representation extractor to process logs without parsing to prevent errors from the parser. The multi-level representations preserve the essential semantics of logs while leaving out insignificant changes in evolving events. EvLog then implements an anomaly discriminator with an attention mechanism to identify the anomalous logs and avoid the issue brought by the unstable sequence. EvLog has shown effectiveness in two real-world system evolution log datasets with an average F1 score of 0.955 and 0.847 in the intra-version setting and inter-version setting, respectively, which outperforms other state-of-the-art approaches by a wide margin. To our best knowledge, this is the first study on localizing anomalous logs over software evolution. We believe our work sheds new light on the impact of software evolution with the corresponding solutions for the log analysis community.