In this work, we propose a novel Parameter-Efficient Fine-Tuning (PEFT) approach based on Gaussian Graphical Models (GGMs), marking the first application of GGMs to PEFT tasks, to the best of our knowledge. The proposed method utilizes the $\ell_{2,g}$-norm to effectively select critical parameters and capture global dependencies. The resulting non-convex optimization problem is efficiently solved using a Block Coordinate Descent (BCD) algorithm. Experimental results on the GLUE benchmark [24] for fine-tuning RoBERTa-Base [18] demonstrate the effectiveness of the proposed approach, achieving competitive performance with significantly fewer trainable parameters. The code for this work is available at: https://github.com/jzheng20/Course projects.git.