Software effort estimation is an important task within software engineering. It is widely used for planning and monitoring software project development as a means to deliver the product on time and within budget. Several approaches for generating predictive models from collected metrics have been proposed throughout the years. Machine learning algorithms, in particular, have been widely-employed to this task, bearing in mind their capability of providing accurate predictive models for the analysis of project stakeholders. In this paper, we propose a grammatical evolution approach for software metrics estimation. Our novel algorithm, namely SEEGE, is empirically evaluated on public project data sets, and we compare its performance with state-of-the-art machine learning algorithms such as support vector machines for regression and artificial neural networks, and also to popular linear regression. Results show that SEEGE outperforms the other algorithms considering three different evaluation measures, clearly indicating its effectiveness for the effort estimation task.