The quest for a model that is able to explain, describe, analyze and simulate real-world complex networks is of uttermost practical as well as theoretical interest. In this paper we introduce and study a network model that is based on a latent attribute structure: each node is characterized by a number of features and the probability of the existence of an edge between two nodes depends on the features they share. Features are chosen according to a process of Indian-Buffet type but with an additional random "fitness" parameter attached to each node, that determines its ability to transmit its own features to other nodes. As a consequence, a node's connectivity does not depend on its age alone, so also "young" nodes are able to compete and succeed in acquiring links. One of the advantages of our model for the latent bipartite "node-attribute" network is that it depends on few parameters with a straightforward interpretation. We provide some theoretical, as well experimental, results regarding the power-law behaviour of the model and the estimation of the parameters. By experimental data, we also show how the proposed model for the attribute structure naturally captures most local and global properties (e.g., degree distributions, connectivity and distance distributions) real networks exhibit. keyword: Complex network, social network, attribute matrix, Indian Buffet process