In this paper, we consider the following boundary-value problems for second-order three-point nonlinear impulsive integro-differential equation of mixed type in a real Banach space E : x ″ ( t ) + f ( t , x ( t ) , x ′ ( t ) , ( A x ) ( t ) , ( B x ) ( t ) ) = θ , t ∈ J , t ≠ t k , Δ x | t = t k = I k ( x ( t k ) ) , Δ x ′ | t = t k = I ̄ k ( x ( t k ) , x ′ ( t k ) ) , k = 1 , 2 , … , m , x ( 0 ) = θ , x ( 1 ) = ρ x ( η ) , where θ is the zero element of E , ( A x ) ( t ) = ∫ 0 t g ( t , s ) x ( s ) d s , ( B x ) ( t ) = ∫ 0 1 h ( t , s ) x ( s ) d s , g ∈ C [ D , R + ] , D = { ( t , s ) ∈ J × J : t ≥ s } , h ∈ C [ J × J , R ] , and Δ x | t = t k denotes the jump of x ( t ) at t = t k , Δ x ′ | t = t k denotes the jump of x ′ ( t ) at t = t k . Some new results are obtained for the existence and multiplicity of positive solutions of the above problems by using the fixed-point index theory and fixed-point theorem in the cone of strict set contraction operators. Meanwhile, an example is worked out to demonstrate the main results.