Existing approaches towards anomaly detection (AD) often rely on a substantial amount of anomaly-free data to train representation and density models. However, large anomaly-free datasets may not always be available before the inference stage; in which case an anomaly detection model must be trained with only a handful of normal samples, a.k.a. few-shot anomaly detection (FSAD). In this paper, we propose a novel methodology to address the challenge of FSAD which incorporates two important techniques. Firstly, we employ a model pre-trained on a large source dataset to initialize model weights. Secondly, to ameliorate the covariate shift between source and target domains, we adopt contrastive training to fine-tune on the few-shot target domain data. To learn suitable representations for the downstream AD task, we additionally incorporate cross-instance positive pairs to encourage a tight cluster of the normal samples, and negative pairs for better separation between normal and synthesized negative samples. We evaluate few-shot anomaly detection on 3 controlled AD tasks and 4 real-world AD tasks to demonstrate the effectiveness of the proposed method.