In this paper, we consider the following nonlinear q-fractional three-point boundary value problem $$\begin{array}{l}(D_{q}^{\alpha}u)(t) + f(t,u(t))=0, \quad 0 < t < 1, 2 < \alpha< 3,\\ [2pt]u(0) = (D_qu)(0) = 0, \quad(D_qu)(1) = \beta(D_qu)(\eta),\end{array}$$ where 0<βηα-2<1. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.