Knowledge Graph Reasoning (KGR) is an effective way to ameliorate sparsity and incompleteness problems by inferring new knowledge based on existing knowledge. The probabilistic case-based reasoning (CBR) model can gather reasoning paths from similar entities and relations in KG, thus outperforming rule-based and embedding-based KGR methods. However, it is still limited by some problems, such as insufficient learning of similarity features and sparse intermediate activations. This paper proposes a \textbf{S}imilarity-\textbf{A}ware graph transformer-enhanced probabilistic CBR model for \textbf{KGR}, namely SA-KGR. The proposed model regards the reasoning task as the KG query answering and is composed of two phases. The first phase is similarity-aware graph transformer-based graph feature encoding, which equips the similarity matrix and Mixture-of-Expert network to obtain fine-grained similarity features that are more helpful for reasoning path generation. The second phase is similarity-enhanced probabilistic case-based reasoning, which can retrieve and infer query answers from the generated candidate paths to complete brain-like cognitive reasoning. Extensive experimental results on various benchmarks unambiguously demonstrate that the proposed SA-KGR model can obtain the state-of-the-art results of current CBR-based methods.