A moving finite element method (MFEM) was applied to the simulation of a pressure swing adsorption (PSA) process based on the local equilibrium model. The PSA process studied is the system of air-5A zeolite for enriching oxygen. Four steps of product pressurization, feed, blowdown, and purge are included in this process. Reasonable agreements are obtained when the theoretical results are compared with the experimental data of Matz and Knaebel (1988). By the property of the moving nodes in MFEM and using small weighting factors, a fixed number of nodes was used to simulate this PSA process, in which a sharp concentration wave forms and moves from the feed end of the column to the product end during the feed step and a simple wave moves in the reverse direction during the purge step. The use of small weighting factors is equivalent to the strong action of the penalty function. The effects of the weighting factors and boundary conditions on the implementation of the MFEM are also discussed.