MATLAB programing language is one of the most popular scientific computing tools, especially for solving linear algebra problems. LU factorization is an essential component for the direct solution of linear equations systems. This paper studied a coarse-grained column agglomeration parallel algorithm in MATLAB to analyze the implementation performance among all the available computation resources. In this paper, we focus on parallelizing the LU decomposition without pivoting algorithm using Gaussian elimination under MATLAB R2020b platform. Numerical experiments were provided to demonstrate the efficiency of CPU parallelization. Performances of the present methods were assessed by comparing the speed and accuracy of different coarse-grained column agglomeration algorithms using different sizes of matrices. Different algorithms were implemented in a four-core Xeon E3-1220 v3 @ 3.10 GHz CPU with 16 GB RAM memory.