With the increasing proliferation of multicore processors, parallelization of applications has become a priority task. In order to take advantage of the multi-core architecture of modern processors, the legacy serial code must be analyzed to discover the regions where the parallelization effort can be more rewarding. This paper presents a parallel implementation of Doolittle Algorithm using OpenMP allowing the users to utilize the multiple cores present in the modern CPUs. The Serial Doolittle Algorithm is analyzed for computing the solution of dense system of linear equations, and is parallelized in C using the OpenMP library which makes it highly efficient, cross-platform compatible and scalable. The performance (speedup) of the Parallel Algorithm on multi-core system has been presented. The experimental results on a multi-core processor show that the proposed Parallel Doolittle Algorithm achieves good performance (speedup)compared to the sequential algorithm.