In this paper, we discuss the existence of positive solutions of the conformable fractional differential equation T α x(t) + f (t, x(t)) = 0, t ∈ [0, 1], subject to the boundary conditions x(0) = 0 and x(1) = λ 1 0 x(t) dt, where the order α belongs to (1, 2], T α x(t) denotes the conformable fractional derivative of a function x(t) of order α, and f : [0, 1] × [0, ∞) → [0, ∞) is continuous. By use of the fixed point theorem in a cone, some criteria for the existence of at least one positive solution are established. The obtained conditions are generally weaker than those derived by using the classical norm-type expansion and compression theorem. A concrete example is given to illustrate the possible application of the obtained results.