Abstract Woven wire screen matrix heat exchanger (WSMHE) is a kind of compact, light-weight and high-efficiency matrix heat exchanger (MHE) for cryogenic applications. This paper presented a numerical model for the design and thermal analysis of WSMHE. The influence of wall thermal resistance, axial conduction, parasitic heat load and properties variation was taken into account, which is neglected in the traditional effectiveness– NTU method but important for compact cryogenic heat exchangers. The proposed numerical method is verified by effectiveness– NTU method under specific conditions, then it is tested according to experiment data, and a well agreement was obtained. Based on this model, a detailed analysis was performed on WSMHEs. The analysis results show that the axial conduction might result in evident decrease of effectiveness at low flow rate region; the effectiveness of WSMHEs with large flow rate could be remarkably enhanced by increasing its length; the influence of parasitic heat load varied little throughout of the flow rate region. Furthermore, the numerical model presented in this paper can be developed to the design and thermal analysis of small partition wall type heat exchangers.