This paper presents the development of a high sensitivity giant magnetoimpedance (GMI) gradiometer, aimed at measuring ultra-weak magnetic fields. Gradiometric configurations are mandatory in order to increase the signal-to-noise ratio in measurements of ultra-weak magnetic fields in unshielded environments. In this work, a first-order GMI gradiometer is designed, based on impedance phase readings of two Co70Fe5Si15B10 amorphous ribbon-shaped samples connected to an electronic circuit that converts magnetic field into an output voltage. In order to optimize the sensitivity and linearity of the GMI samples, they must be biased at a given magnetic field. The gradiometer should provide voltage values proportional only to the field gradient between the samples, generated by a magnetic source, and not due to variations resulting from the change in the biasing field. Then, a control loop was designed to reduce the influence of magnetic interference over the biasing magnetic field. This paper describes the electronic circuit developed to implement the proposed GMI gradiometer and analyzes its performance by computational simulations.