Axions are a compelling dark matter candidate suggested by theories beyond the Standard Model. The predicted axion-electron coupling and the resulting pseudomagnetic field allow for laboratory axion searches. Here we report an experimental axion search via a superconductor-spin hybrid magnetometer. A state-of-the-art broadband magnetometer with a sensitivity of sub-100 aT/Hz^{1/2} at tens of kHz has been realized by coupling a ferrite spin sensor to a readout system based on a superconducting quantum interference device. The most stringent terrestrial constraints on the axion-electron coupling have been established in the frequency range 5∼60 kHz. In the future, an improvement on the constraints of more than 4 orders of magnitude is foreseeable through arrays of superconductor-spin hybrid magnetometers with optimized designs. This work demonstrates the potential of superconductor-spin hybrid magnetometers in high-precision magnetic field sensing and the study of fundamental physics.