In recent years, unsupervised person re-identification (re-ID) has attracted a lot of attention because it can save manual annotation costs and adapt to new scenes more conveniently in real-world applications. We focus on fully unsupervised learning-based re-ID, which aims to train a discriminative model based on unlabeled person images. In unsupervised learning, we need to generate pseudo labels by clustering convolutional features and then train convolutional neural network (CNN) models with these pseudo labels. The features used in the clustering process play an important role to ensure the quality of pseudo labels. Hence, we propose an enhancing feature extraction method to increase the reliability of generated pseudo labels and thus facilitate CNN model training. In order to enrich the obtained features, we carry out the feature extraction from both global and local aspects. The global features are extracted with ResNet50 backbone as many existing methods do. The local features are extracted by an additional part-based feature pyramid structure, in which the person image is divided into three parts and the features are extracted from each part with a pyramid structure. Then, we fuse the multi-layer pyramid features for each part as the local features. According to the joint global features and local features, the pseudo labels are predicted using clustering algorithms and further refined based on the similarity between global and local features. In addition, we design an inter-camera association learning component to effectively learn the ID discrimination ability across cameras. Extensive experiments on three large and representative person re-ID datasets demonstrate the effectiveness of the proposed approach.