Sparse Matrix-Vector Multiplication (SpMV) has become a critical performance bottleneck in the local deployment of sparse Large Language Models (LLMs), where inference predominantly operates on workloads during the decoder phase with a batch size of one. Existing SpMV kernels and sparse matrix formats, originally designed for scientific computing, fail to exploit the unique structure patterns inherent in sparse LLMs, resulting in suboptimal performance and excessive storage overhead. This paper presents EC-SpMV, a GPU-optimized SpMV approach for accelerating sparse LLM inference. EC-SpMV introduces (1) a hierarchical block extraction algorithm that captures multiple granularities of block structures within sparse LLMs, and (2) a novel compressed sparse format (EC-CSR) that employs delta indexing to reduce storage overhead and enhance memory access efficiency. Evaluated on real sparse weight matrices from LLaMA and OPT models, EC-SpMV achieves up to 6.44x speedup over state-of-the-art SpMV libraries and reduces storage overhead by up to 55.4% compared to CSR.