Let H=(V,E) be an r-uniform hypergraph. For each 1≤s≤r−1, an s-path Pnr,s of length n in H is a sequence of distinct vertices v1,v2,…,vs+n(r−s) such that {v1+i(r−s),…,vs+(i+1)(r−s)}∈E(H) for each 0≤i≤n−1. Recently, the Ramsey number of 1-paths in uniform hypergraphs has received a lot of attention. In this paper, we consider the Ramsey number of r/2-paths for even r. Namely, we prove the following exact result: R(Pnr,r/2,P3r,r/2)=R(Pnr,r/2,P4r,r/2)=(n+1)r2+1.