Spoken language understanding (SLU) is an essential task for machines to understand human speech for better interactions. However, errors from the automatic speech recognizer (ASR) usually hurt the understanding performance. In reality, ASR systems may not be easy to adjust for the target scenarios. Therefore, this paper focuses on learning utterance representations that are robust to ASR errors using a contrastive objective, and further strengthens the generalization ability by combining supervised contrastive learning and self-distillation in model fine-tuning. Experiments on three benchmark datasets demonstrate the effectiveness of our proposed approach.