This paper presents our solution for optimization task of the 3rd ACM-China IPCC. By the complexity analysis, we identified three time-consuming subroutines of original algorithm: marking edges, computing pseudo inverse and sorting edges. These subroutines becomes the main performance bottleneck owing to their super-linear time complexity. To address this, we proposed LGRASS, a linear graph spectral sparsification algorithm to run in strictly linear time. LGRASS takes advantage of spanning tree properties and efficient algorithms to optimize bottleneck subroutines. Furthermore, we crafted a parallel processing scheme for LGRASS to make full use of multi-processor hardware. Experiment shows that our proposed method fulfils the task in dozens of milliseconds on official test cases and keep its linearity as graph size scales up on random test cases.