The problem of simultaneously predicting multiple real-valued outputs using a shared set of input variables is known as multi-target regression and has attracted considerable interest in the past couple of years. The dominant approach in the literature for multi-target regression is to capture the dependencies between the outputs through a linear model and express it as an output mixing matrix. This modelling formalism, however, is too simplistic in real-world problems where the output variables are related to one another in a more complex and non-linear fashion. To address this problem, in this study, we propose a structural modelling approach where the correlations between output variables are modelled using a non-linear approach. In particular, we pose the multi-target regression problem as one of vector-valued composition function learning in the reproducing kernel Hilbert space and propose a non-linear structure learning approach to capture the relationship between the outputs via an output kernel. By virtue of using a non-linear output kernel function, the proposed approach can better discover non-linear dependencies among targets for improved prediction performance. An extensive evaluation conducted on different databases reveals the benefits of the proposed multi-target regression technique against the baseline and the state-of-the-art methods.