In order to alleviate the computational burden associated with superlinear compute scalings with molecular size in electron correlation methods, researchers have developed local correlation methods that wisely treat relatively small contributions as zeros but still yield accurate energy approximation. Such local correlation techniques can also be combined with parallel computing resources to obtain further efficiency and scalability. This work focuses on the distributed memory parallel implementation of a local correlation method for second order Mo̷ller-Plesset (MP2) theory. This method also only has a single threshold to control the dropping of terms and accuracy of different computing kernels in the algorithm. The process partitioning strategy and distributed parallel implementation with the message passing interface (MPI) are discussed. In particular, the algorithm relies on a fixed sparsity pattern matrix multiplication and a corresponding distributed conjugate gradient solver, which exhibits almost linear scaling in both strong and weak scaling analyses. Numerical experiments on a range of molecules, including linear chains and molecules with 2 and 3-dimensional characters, are reported. For example, with only 32 MPI ranks, this MP2 implementation can calculate the correlation energy of vancomycin in def2-TZVP basis within 0.003% accuracy (10-6.5 threshold) in half an hour, where the same problem is unfeasible to solve with sequential or pure shared memory implementations.