Speculative decoding (SPD) has emerged as a promising technique to accelerate Large Language Model (LLM) inference. However, current approaches typically enforce a uniform verification standard, neglecting the inherent heterogeneity of natural language and failing to distinguish between semantically-rich content and structurally-predictable syntax. In this paper, we propose LinguaSpec, a training-free framework that leverages linguistic priors to enable adaptive drafting and verification. Specifically, we introduce: (1) a Static Linguistic Probe (SLP) to categorize tokens with zero latency; (2) Syntactic Normalized Surprisal (SNS) to calibrate uncertainty against category-specific entropy; and (3) a dual strategy of Syntactically-Guided Elastic Expansion and POS-Adaptive Deferred Verification to dynamically adjust drafting depth and verification rigor. By balancing semantic integrity with structural efficiency, LinguaSpec significantly accelerates inference without requiring additional training. Experimental results demonstrate its superior performance across diverse benchmarks.