Biomagnetic signals, mostly due to the electrical activity in the body, are very weak and they can only be detected by the most sensitive magnetometers, such as Superconducting Quantum Interference Devices (SQUIDs). We report here biomagnetic recordings with hybrid sensors based on Giant MagnetoResistance (GMR). We recorded magnetic signatures of the electric activity of the human heart (magnetocardiography) in healthy volunteers. The P-wave and QRS complex, known from the corresponding electric recordings, are clearly visible in the recordings after an averaging time of about 1 min. Multiple recordings at different locations over the chest yielded a dipolar magnetic field map and allowed localizing the underlying current sources. The sensitivity of the GMR-based sensors is now approaching that of SQUIDs and paves way for spin electronics devices for functional imaging of the body.