We have developed a novel method to accurately detect QRS complex peaks using the variable frequency complex demodulation (VFCDM) method. The approach's novelty stems from reconstructing an ECG signal using only the frequency components associated with the QRS waveforms by VFCDM decomposition. After signal reconstruction, both top and bottom sides of the signal are used for peak detection, after which we compare locations of the peaks detected from both sides to ensure false peaks are minimized. Finally, we impose position-dependent adaptive thresholds to remove any remaining false peaks from the prior step. We applied the proposed method to the widely benchmarked MIT-BIH arrhythmia dataset, and obtained among the best results compared to many of the recently published methods. Our approach resulted in 99.94% sensitivity, 99.95% positive predictive value and a 0.11% detection error rate. Three other datasets-the MIMIC III database, University of Massachusetts atrial fibrillation data, and SCUBA diving in salt water ECG data-were used to further test the robustness of our proposed algorithm. For all these three datasets, our method retained consistently higher accuracy when compared to the BioSig Matlab toolbox, which is publicly available and known to be reliable for ECG peak detection.