Aims/ The aims of this paper are to prove existence and uniqueness of following integral boundary conditions mixed problem for parabolic equation : ∂u ∂t − a(t) xn+1 ∂ ∂x ( x ∂u ∂x ) + bu = θ(x, t), u(x, 0) = λ(x), 0 ≤ x ≤ `, ∫ ` 0 xu(x, t) dx = En(t), 0 ≤ t ≤ T , ∫ ` 0 xu(x, t) dx = Gn(t), 0 ≤ t ≤ T. The proofs are based on a priori estimates established in Sobolev function spaces and Fourier’s method.