Astronomical outliers, such as unusual, rare or unknown types of astronomical objects or phenomena, constantly lead to the discovery of genuinely unforeseen knowledge in astronomy. More unpredictable outliers will be uncovered in principle with the increment of the coverage and quality of upcoming survey data. However, it is a severe challenge to mine rare and unexpected targets from enormous data with human inspection due to a significant workload. Supervised learning is also unsuitable for this purpose since designing proper training sets for unanticipated signals is unworkable. Motivated by these challenges, we adopt unsupervised machine learning approaches to identify outliers in the data of galaxy images to explore the paths for detecting astronomical outliers. For comparison, we construct three methods, which are built upon the k-nearest neighbors (KNN), Convolutional Auto-Encoder (CAE)+ KNN, and CAE + KNN + Attention Mechanism (attCAE KNN) separately. Testing sets are created based on the Galaxy Zoo image data published online to evaluate the performance of the above methods. Results show that attCAE KNN achieves the best recall (78%), which is 53% higher than the classical KNN method and 22% higher than CAE+KNN. The efficiency of attCAE KNN (10 minutes) is also superior to KNN (4 hours) and equal to CAE+KNN(10 minutes) for accomplishing the same task. Thus, we believe it is feasible to detect astronomical outliers in the data of galaxy images in an unsupervised manner. Next, we will apply attCAE KNN to available survey datasets to assess its applicability and reliability.