This article discusses the solution of one-dimensional convection-diffusion equations by using Successive Over-Relaxation Red Black (SORRB) and Gauss-Seidel Red Black (GSRB) method for parallel and sequential. The implementation for this method has been performed on parallel computers for distributed memory systems using Parallel Virtual Machine (PVM) and C which used 18 personal computers with Intel Pentium IV processor. This research successfully results in affirmation of the theories presented by Foster (1995) which proposed that the percentage of efficiency decreases and the speedup factor increases when the numbers of processors are increasing. The research result also shows that the parallelization of GSRB and SORRB method is faster than sequential especially when the number ofprocessors increased. As a conclusion, problem solving by using parallelization will reduce execution time especially in solving large scale problems