System logs record detailed information about system operation and are important for analyzing the system's operational status and performance. Rapid and accurate detection of system anomalies is of great significance to ensure system stability. However, large-scale distributed systems are becoming more and more complex, and the number of system logs gradually increases, which brings challenges to analyze system logs. Some recent studies show that logs can be unstable due to the evolution of log statements and noise introduced by log collection and parsing. Moreover, deep learning-based detection methods take a long time to train models. Therefore, to reduce the computational cost and avoid log instability we propose a new Word2Vec-based log unsupervised anomaly detection method (LogUAD). LogUAD does not require a log parsing step and takes original log messages as input to avoid the noise. LogUAD uses Word2Vec to generate word vectors and generates weighted log sequence feature vectors with TF-IDF to handle the evolution of log statements. At last, a computationally efficient unsupervised clustering is exploited to detect the anomaly. We conducted extensive experiments on the public dataset from Blue Gene/L (BGL). Experimental results show that the F1-score of LogUAD can be improved by 67.25% compared to LogCluster.