The ionosphere delay error is one of mainly measure distance error to satellite receiver. It is difficult to describe truly status of ionosphere, because lots of factor will influence the status. In this paper, several commonly used ionosphere delay correction model, including Bent model, IRI model, Klubuchar model, NeQuick model and IGGSH model are discussed and the correction result of position error is analyzed by using the single frequency GPS receiver data. The result of statistical analysis and simulation provide a reference for the single frequency GPS receiver user to select the suitable ionosphere delay correction model