Background Simultaneous electroencephalography (EEG) and functional magnetic resonance image (fMRI) acquisitions provide better insight into brain dynamics. Some artefacts due to simultaneous acquisition pose a threat to the quality of the data. One such problematic artefact is the ballistocardiogram (BCG) artefact. Methods We developed a hybrid algorithm that combines features of empirical mode decomposition (EMD) with principal component analysis (PCA) to reduce the BCG artefact. The algorithm does not require extra electrocardiogram (ECG) or electrooculogram (EOG) recordings to extract the BCG artefact. Results The method was tested with both simulated and real EEG data of 11 participants. From the simulated data, the similarity index between the extracted BCG and the simulated BCG showed the effectiveness of the proposed method in BCG removal. On the other hand, real data were recorded with two conditions, i.e. resting state (eyes closed dataset) and task influenced (event-related potentials (ERPs) dataset). Using qualitative (visual inspection) and quantitative (similarity index, improved normalized power spectrum (INPS) ratio, power spectrum, sample entropy (SE)) evaluation parameters, the assessment results showed that the proposed method can efficiently reduce the BCG artefact while preserving the neuronal signals. Comparison with existing methods Compared with conventional methods, namely, average artefact subtraction (AAS), optimal basis set (OBS) and combined independent component analysis and principal component analysis (ICA-PCA), the statistical analyses of the results showed that the proposed method has better performance, and the differences were significant for all quantitative parameters except for the power and sample entropy. Conclusions The proposed method does not require any reference signal, prior information or assumption to extract the BCG artefact. It will be very useful in circumstances where the reference signal is not available. © 2017 Elsevier B.V.