Temporal Video Grounding (TVG), the task of locating specific video segments based on language queries, is a core challenge in long-form video understanding. While recent Large Vision-Language Models (LVLMs) have shown early promise in tackling TVG through supervised fine-tuning (SFT), their abilities to generalize remain limited. To address this, we propose a novel post-training framework that enhances the generalization capabilities of LVLMs via reinforcement learning (RL). Specifically, our contributions span three key directions: (1) Time-R1: we introduce a reasoning-guided post-training framework via RL with verifiable reward to enhance the capabilities of LVLMs on the TVG task. (2) TimeRFT: we explore data-efficient post-training strategies on our curated RL-friendly dataset, which trains the model to progressively comprehend difficult samples, leading to better generalization. (3) TVGBench: we carefully construct a small yet comprehensive benchmark for LVLM evaluation, assessing 11 types of queries and featuring balanced distributions across both videos and queries. Extensive experiments demonstrate that Time-R1 achieves state-of-the-art performance across multiple downstream datasets using only 2.5K training data, while improving its general video understanding capabilities.