In this paper, we are concerned with the following eigenvalue problems of m-point boundary value problem for p-Laplacian dynamic equation on time scales $(varphi_p(u^{Delta}(t)))^ abla+{lambda}h(t)f(u(t))=0,;tin(0,T)$, $u(0)=0,varphi_p(u^{Delta}(T))=sumlimits_{i=1}^{m-2}a_ivarphi_p(u^{Delta}(xi_i))$, where $varphi_p(u)=|u|^{p-2}$u, p > 1 and $lambda$ > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solution and nonexistence are obtained for $lambda$ evaluated in different intervals. Our work develop and improve many known results in the literature even for the continual case. In doing so the usual restriction that $f_0=lim_{u{ ightarrow}0}+f(u)/varphi_p(u)$ and $f_infty = lim_{u{ ightarrow}{infty}}f(u)/varphi_p({u})$ exist is removed. As an applications, an example is given to illustrate the main results obtained.