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In the present paper, we mainly study the integrable semi-discretization of amulti-component short pulse equation. Firstly, we briefly review the bilinearequations for a multi-component short pulse equation proposed by Matsuno (J.Math. Phys. \textbf{52} 123705) and reaffirm its $N$-soliton solution in termsof pfaffians. Then by using a B\"{a}cklund transformation of the bilinearequations and defining a discrete hodograph (reciprocal) transformation, anintegrable semi-discrete multi-component short pulse equation is constructed.Meanwhile, its $N$-soliton solution in terms of pfaffians is also proved.

Integrable semi-discretization of a multi-component short pulse equation