The recent advancements of Large Language Models (LLMs) have spurred considerable research interest in extending their linguistic capabilities beyond text to other modalities, which leads to emergence of speech-based LLMs (SpeechLMs) with capability of processing user request in either speech or textual formats. However, owing to inter-modal discrepancies, these SpeechLMs still exhibit a significant performance gap compared to their text-based LLM counterparts in instruction-following, particularly when confronted with the dynamic and variable nature of user speech. To address this challenge, this paper introduces a framework termed Reinforced Behavior Alignment (RBA), designed to bolster the language generation proficiency of SpeechLMs. Instead of relying on supervised fine-tuning from human annotations, RBA employs a self-synthesis methodology to generate extensive, high-fidelity alignment data by a powerful teacher LLM. Then SpeechLMs is aligned its behavior with that of a teacher using a reinforcement learning-based approach. Experimental results demonstrate that this method effectively enhances the instruction-following capabilities of SpeechLMs that outperform conventional distillation baselines. Crucially, we demonstrate that RBA can be seamlessly extended to tasks such including spoken question answering and speech-to-text translation, attaining state-of-the-art performance on open benchmarks with only self-generated data.