In this paper, the existence and multiplicity of positive solutions for a class
of non-resonant fourth-order integral boundary value problem

with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem, where $f ∈ C$ ([0, 1]×[0, +∞)×(−∞, 0], [0, +∞)), $q(t)∈L$^{1}[0, 1]
is nonnegative, $α, β ∈ R$ and satisfy $β < 2π$^{2}, $α$ > 0, $α/π$^{4} + $β/π$^{2} < 1, $λ$_{1,2} =
(−$β$ ∓ $\sqrt{β^2 + 4α}$)/2. The corresponding examples are raised to demonstrate
the results we obtained.