While human evaluation is the most reliable metric for evaluating speech generation systems, it is generally costly and time-consuming. Previous studies on automatic speech quality assessment address the problem by predicting human evaluation scores with machine learning models. However, they rely on supervised learning and thus suffer from high annotation costs and domain-shift problems. We propose SpeechLMScore, an unsupervised metric to evaluate generated speech using a speech-language model. SpeechLMScore computes the average log-probability of a speech signal by mapping it into discrete tokens and measures the average probability of generating the sequence of tokens. Therefore, it does not require human annotation and is a highly scalable framework. Evaluation results demonstrate that the proposed metric shows a promising correlation with human evaluation scores on different speech generation tasks including voice conversion, text-to-speech, and speech enhancement.