We introduce matched-filter fMRI, which improves BOLD (blood oxygen level dependent) sensitivity by variable-density image acquisition tailored to subsequent image smoothing. Image smoothing is an established post-processing technique used in the vast majority of fMRI studies. Here we show that the signal-to-noise ratio of the resulting smoothed data can be substantially increased by acquisition weighting with a weighting function that matches the k-space filter imposed by the smoothing operation. We derive the theoretical SNR advantage of this strategy and propose a practical implementation of 2D echo-planar acquisition matched to common Gaussian smoothing. To reliably perform the involved variable-speed trajectories, concurrent magnetic field monitoring with NMR probes is used. Using this technique, phantom and in vivo measurements confirm reliable SNR improvement in the order of 30% in a "resting-state" condition and prove robust in different regimes of physiological noise. Furthermore, a preliminary task-based visual fMRI experiment equally suggests a consistent BOLD sensitivity increase in terms of statistical sensitivity (average t-value increase of about 35%). In summary, our study suggests that matched-filter acquisition is an effective means of improving BOLD SNR in studies that rely on image smoothing at the post-processing level.