We study the one-dimensional p-Laplacian m-point boundary value problem (φp(uΔ(t)))Δ+a(t)f(t,u(t))=0, t∈[0,1]T, u(0)=0, u(1)=∑i=1m−2aiu(ξi), where T is a time scale, φp(s)=|s|p−2s, p>1, some new results are obtained for the existence of at least one, two, and three positive solution/solutions of the above problem by using Krasnosel′skll′s fixed point theorem, new fixed point theorem due to Avery and Henderson, as well as Leggett-Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian m-point boundary value problem on time scales has been studied.