We have measured the magnetic susceptibility X of Sr14-yYyCu24O41-δ consisting of two-dimensional Cu2O3 planes, namely, so-called spin-1/2 ladders with two legs and also of one-dimensional CuO2 chains. The susceptibility Xchain(T) due to the CuO2 chains, obtained by subtracting the susceptibility Xladder(T) due to the Cu2O3 planes from the experimental data of X(T), is described by the Curie-Weiss law at T > Tmax ∼ 80 K, where X exhibits the maximum for y = 0. With increasing y, Xchain becomes large owing to the increase of Cu2+ spins introduced into the CuO2 chains. Moreover, the antiferromagnetic interaction between Cu2+ spins in the CuO2 chains becomes weak with the increase in y, namely, with the increase of Cu2+ spins introduced into the CuO2 chains, leading to suppression of the spin gap of the CuO2 chains. As the result, the broad peak of X, observed around 80 K for y = 0, is found to disappear for y ≥ 1.0.