Video Large Language Models (Video-LLMs) excel in video understanding but suffer from high inference latency during autoregressive generation. Speculative Decoding (SD) mitigates this by applying a draft-and-verify paradigm, yet existing methods are constrained by rigid exact-match rules, severely limiting the acceleration potential. To bridge this gap, we propose LVSpec, the first training-free loosely SD framework tailored for Video-LLMs. Grounded in the insight that generation is governed by sparse visual-relevant anchors (mandating strictness) amidst abundant visual-irrelevant fillers (permitting loose verification), LVSpec employs a lightweight visual-relevant token identification scheme to accurately pinpoint the former. To further maximize acceptance, we augment this with a position-shift tolerant mechanism that effectively salvages positionally mismatched but semantically equivalent tokens. Experiments demonstrate that LVSpec achieves high fidelity and speed: it preserves >99.8 of target performance while accelerating Qwen2.5-VL-32B by 2.70x and LLaVA-OneVision-72B by 2.94x. Notably, it boosts the mean accepted length and speedup ratio by 136% and 35% compared to SOTA training-free SD methods for Video-LLMs.