The performance of a superconducting quantum interference device (SQUID) gradiometer is always determined by its pick-up coil geometry, such as baseline and radius. In this paper, based on the expressions for the coupled flux threading a magnetometer obtained by Wikswo, we studied how the gradiometer performance parameters, including the current dipole sensitivity, spatial resolution and signal-to-noise ratio (SNR), are affected by its pick-up coil via MatLab simulation. Depending on the simulation results, the optimal pick-up coil design region for a certain gradiometer can be obtained. To verify the simulation results, we designed and fabricated several first-order gradiometers based on the weakly damped SQUID with different pick-up coils by applying superconducting connection. The experimental measurements were conducted on a simple current dipole in a magnetically shielding room. The measurement results are well in coincidence with the simulation ones, indicating that the simulation model is useful in specific pick-up coil design.