Modeling the hemodynamic response in functional magnetic resonance (fMRI) experiments is an important aspect of the analysis of functional neuroimages. This has been done in the past using parametric response function, from a limited family. In this contribution, the authors adopt a semi-parametric approach based on finite impulse response (FIR) filters. In order to cope with the increase in the number of degrees of freedom, the authors introduce a Gaussian process prior on the filter parameters. They show how to carry on the analysis by incorporating prior knowledge on the filters, optimizing hyper-parameters using the evidence framework, or sampling using a Markov Chain Monte Carlo (MCMC) approach. The authors present a comparison of their model with standard hemodynamic response kernels on simulated data, and perform a full analysis of data acquired during an experiment involving visual stimulation.