Let HV be the loop Heisenberg-Virasoro Lie algebra over ℂ with basis {Lα,i, Hβ,j∣α, β, i, j ∈ ℤ} and brackets [Lα,i, Lβ,j] = (α − β) Lα+β,i+j, [Lα,i, Hβ,j] = − βHα+β,i+j, [Hα,i, Hβ,j] = 0. In this paper, a formal distribution Lie algebra of HV is constructed. Then, the associated conformal algebra CHV is studied, where CHV has a ℂ[∂]-basis {Li, Hi∣i ∈ ℤ} with λ-brackets [Li λ Lj] = (∂ + 2λ) Li+j, [Li λ Hj] = (∂ + λ) Hi+j, [Hi λ Lj] = λLi+j, and [Hi λ Hj] = 0. In particular, the conformal derivations of CHV are determined. Finally, rank one conformal modules and ℤ-graded free intermediate series modules over CHV are classified.