This paper studies the problem of unsupervised time series representation learning, which aims to map unlabeled time series data into a low-dimensional latent space for various downstream tasks. Previous works usually combine a range of augmentation strategies with contrastive learning to generate discriminative representations. However, these augmentation strategies could alter the original semantics of time series data, which could degrade the performance of representation learning. To solve this problem, this paper incorporates the large language model (LLM) agent to guide unsupervised time series representation learning and proposes a novel framework named Multi-Agent Collaboration for Time-series Representation Learning (MERIT). The core of our MERIT is to utilize three LLM agents to collaboratively generate positive views for time series data. In particular, we first design a retrieval agent to automatically identify the relevant time series data from a coarse candidate set. Then, these selected sequences are further utilized to enhance an augmentation agent which automatically selects reliable augmentation strategies from an augmentation strategy library. We also design a review agent to evaluate the quality of generated views and stop the generation process. These three agents are designed to work in a loop for effective time series representation learning. Extensive experiments on multiple time series datasets demonstrate the effectiveness of our MERIT in comparison with state-of-the-art baselines.