We examined the effectiveness of an infinite cylindrical superconducting impurity of radius a in an infinite type-II superconductor as a pinning center. The impurity and the superconducting background have the penetration depth λ i and λ s , respectively. With regard to a single-quantum vortex, the free energy of the system and the pinning potential for a vortex were calculated, based upon the London model of the vortex line. Here, the pinning potential U p i n is defined by the difference between the free energy of a vortex being at the center of the impurity and that being infinitely distant from the impurity. U p i n is negative for λ i > λ s . On the other hand, U p i n is positive for λ i < λ s . In the limit of a λ i and λ s , the pinning potential is found to be U p i n = φ 0 2 (1/λ i 2 - 1/λ s 2 ) ln κ/4πμ 0 . In the limit of a λ i and λ s , the pinning potential is found to be U p i n = φ 0 2 [(1/λ i 2 - 1/λ s s 2 ) ln κ + (1/λ s s 2 ) ln(λ s /a) - (1/λ i 2 ) ln(λ i /a)]/4πμ 0 . There is a clear correlation between the intrinsic property of these two superconducting materials and the pinning potential.