The growing interest in language-conditioned robot manipulation aims to develop robots capable of understanding and executing complex tasks, with the objective of enabling robots to interpret language commands and manipulate objects accordingly. While language-conditioned approaches demonstrate impressive capabilities for addressing tasks in familiar environments, they encounter limitations in adapting to unfamiliar environment settings. In this study, we propose a general-purpose, language-conditioned approach that combines base skill priors and imitation learning under unstructured data to enhance the algorithm's generalization in adapting to unfamiliar environments. We assess our model's performance in both simulated and real-world environments using a zero-shot setting. In the simulated environment, the proposed approach surpasses previously reported scores for CALVIN benchmark, especially in the challenging Zero-Shot Multi-Environment setting. The average completed task length, indicating the average number of tasks the agent can continuously complete, improves more than 2.5 times compared to the state-of-the-art method HULC. In addition, we conduct a zero-shot evaluation of our policy in a real-world setting, following training exclusively in simulated environments without additional specific adaptations. In this evaluation, we set up ten tasks and achieved an average 30% improvement in our approach compared to the current state-of-the-art approach, demonstrating a high generalization capability in both simulated environments and the real world. For further details, including access to our code and videos, please refer to https://hk-zh.github.io/spil/