A one-dimensional model about the ignition process of boron particle in boron-based propellant ducted rocket is systemically investigated. The gas flow around the boron particle, the heat transfer and the mass transfer between the boron particle and the surrounding are included in the model. And the effects of Stefan flow are also proposed. The changing regularities of important parameters in the two typical cases, viz., the successful ignition case and the degenerate ignition case are studied in detail. And their reasons are analyzed. The result shows that both the evaporation of the liquid boric oxide layer and the oxidation of the boron are remarkably accelerated as the result of the self-heating exothermic oxidation in the successful ignition case, and the mass fraction profiles of the oxygen gas and those of the B2O3 gas also dramatically change in that case. However, both the mass flux of the evaporation of the liquid boric oxide layer and that of the consumption of the oxygen gas are relatively small, and both of them tend to be nearly constant in the degenerate ignition case. The mass fraction profile of the oxygen gas and that of the B2O3 gas change little in the degenerate ignition case. In the two typical cases, Stefan flow on the boron particle surface undergoes the change of flow direction, viz., Stefan flow initially comes from the surrounding and then it flows from the particle surface to the surrounding.