We consider quantum transport on generalized scale-free networks (GSFNs) in the continuous-time quantum walk (CTQW) model. The efficiency of the transport is monitored through the exact and the average return probabilities. In this model these probabilities are fully determined by the eigenvalues and eigenvectors of the connectivity matrix. In the case of GSFNs we observe a nontrivial interplay between strong localization effects, due to starlike segments, and good spreading because of the linear segments. We show that the quantum transport on GSFNs can be increased by varying the minimum or the maximum allowed degrees, i.e., the limiting number of links emerging from every node. The same quantum efficiency is reached by considering various combinations of the construction parameters of the network, which normally show different topological features.