Video Large Language Models (Video-LLMs) have recently shown strong performance in basic video understanding tasks, such as captioning and coarse-grained question answering, but struggle with compositional reasoning that requires multi-step spatio-temporal inference across object relations, interactions, and events. The hurdles to enhancing this capability include extensive manual labor, the lack of spatio-temporal compositionality in existing data and the absence of explicit reasoning supervision. In this paper, we propose STEP, a novel graph-guided self-training method that enables Video-LLMs to generate reasoning-rich fine-tuning data from any raw videos to improve itself. Specifically, we first induce Spatio-Temporal Scene Graph (STSG) representation of diverse videos to capture fine-grained, multi-granular video semantics. Then, the STSGs guide the derivation of multi-step reasoning Question-Answer (QA) data with Chain-of-Thought (CoT) rationales. Both answers and rationales are integrated as training objective, aiming to enhance model's reasoning abilities by supervision over explicit reasoning steps. Experimental results demonstrate the effectiveness of STEP across models of varying scales, with a significant 21.3\% improvement in tasks requiring three or more reasoning steps. Furthermore, it achieves superior performance with a minimal amount of self-generated rationale-enriched training samples in both compositional reasoning and comprehensive understanding benchmarks, highlighting the broad applicability and vast potential.