A model is considered well-calibrated when its probability estimate aligns with the actual likelihood of the output being correct. Calibrating language models (LMs) is crucial, as it plays a vital role in detecting and mitigating hallucinations of LMs as well as building more trustworthy models. However, standard calibration techniques may not be suited for LM calibration. For instance, post-processing methods such as temperature scaling do not reorder the candidate generations. On the other hand, training-based methods require fine-tuning the entire model, which is impractical for LMs of large scale. We present LitCab, a lightweight calibration mechanism consisting of a single linear layer that takes the input text representation and predicts a bias term, which is then added to the LM output logits. LitCab improves model calibration by only adding < 2% of the original model parameters. For evaluation, we construct CaT, a benchmark consisting of eight text generation tasks, covering responses ranging from short phrases to paragraphs. We test LitCab with Llama2-7B, where it improves calibration across all tasks, reducing the average ECE score by as large as 30%. We further conduct a comprehensive evaluation with multiple popular open-sourced LMs from GPT and LLaMA families, yielding the following key findings: (i) Larger models within the same family exhibit better calibration on tasks with short generation tasks, but not necessarily for longer ones. (ii) GPT-family models show superior calibration compared to LLaMA, Llama2, and Vicuna models, despite having much fewer parameters. (iii) Fine-tuning pretrained model (e.g., LLaMA) with samples of limited purpose (e.g., conversations) may lead to worse calibration, highlighting the importance of fine-tuning setups for calibrating LMs.