Frosting problem restricts the wide application of heat pump, and direct expansion solar-assisted heat pump system (DX-SAHP) can be a solution. However, research on DX-SAHP for space heating under frosting conditions is rare in the published literatures, especially on numerical level. A dynamic model for a DX-SAHP system for space heating is proposed and validated in this paper. The root mean square deviations of the simulation results from the experimental data are no more than 6%, which validates the model. Based on the model, the frost characteristics are investigated and parametric analysis is conducted. Compared to the widely used air source heat pumps with fin-and-tube heat exchangers, the frost pattern of the evaporator-collector is nearly steady and the frosting rate is less. The analyzed parameters include ambient temperature, solar irradiation and relative humidity. Solar irradiation can retard frosting and improve the heating performance of the DX-SAHP system. Solar irradiance of 100W/m(2) can totally prevent frost formation as the ambient temperature and the relative humidity is -1 degrees C and 70%, respectively. Under the condition that the relative humidity and solar irradiance are 70% and 0W/m(2), frost is the most serious with the ambient temperature of -1 degrees C, with higher heating capacity and COP comparing to that under other ambient temperatures. No frost forms when the ambient temperature and solar irradiance are 1 degrees C and 0W/m(2), and the relative humidity is lower than 60%. When the relative humidity is over 60%, the frost thickness and the heating performance increase with increasing relative humidity. The frosting process is found to be beneficial for the heating performance of the system. The results indicate that the DX-SAHP system is applicable under frosting conditions. (C) 2019 Elsevier B.V. All rights reserved.