The Japan Atomic Energy Research Institute, JAERI, has started drafting a construction program for the “Positron Factory”, in which linac-based intense monoenergetic positron beams are planned to be applied to materials characterization and basic research. A tentative goal of the slow positron beam intensity is 10 10s −1. A rough and conservative estimate based on the empirical data has shown that this intensity can be attained with a linac of 100 kW class with a beam energy of around 100 MeV. In this article a new concept of the slow beam production system is demonstrated, which is expected to supply such intense beams for more than two positron beam lines simultaneously, on the basis of a Monte Carlo simulation. The design of a target suitable for the high power linac is also proposed.