The slow positron beam system is an important device in the study of positron physics and techniques, especially in materials research. This paper presents obtained results in studying and applying a charged particles trajectory simulation program – Simion for building feasible design models for the system. The built models with different designs based on reference designs of some typical systems include a straight-shaped model, a 500 bent-shaped model and a 900 bent-shaped model. Some positron beam trajectory calculation tests have been performed for comparison between the models. From the tests, the 500 bent-shaped model has been proposed as a conceptual design for building a real slow positron beam system in the future in Vietnam.