This paper introduces a novel generalized self-imitation learning GSIL framework, which effectively and efficiently aligns large language models with offline demonstration data. We develop GSIL by deriving a surrogate objective of imitation learning with density ratio estimates, facilitating the use of self-generated data and optimizing the imitation learning objective with simple classification losses. GSIL eliminates the need for complex adversarial training in standard imitation learning, achieving lightweight and efficient fine-tuning for large language models. In addition, GSIL encompasses a family of offline losses parameterized by a general class of convex functions for density ratio estimation and enables a unified view for alignment with demonstration data. Extensive experiments show that GSIL consistently and significantly outperforms baselines in many challenging benchmarks, such as coding (HuamnEval), mathematical reasoning (GSM8K) and instruction-following benchmark (MT-Bench). Code is public available at https://github.com/tengxiao1/GSIL.