We introduce a new two-stage Half-Sweep Modified Arithmetic Mean (HSMAM) method for the solution of elliptic equation in two space dimensions. It is based on the combination of Half-Sweep (HS) iteration procedure and the Modified Arithmetic Mean (MAM) method. This iterative method converges faster than the existing variants of Arithmetic Method (AM) method. The method is very suitable for parallel implementation on a multiprocessor system. Some numerical experiments are carried out to demonstrate the efficiency of the proposed method for solving elliptic partial differential equation. Also, the performances of the existing variants of AM method are included for comparison purposes.