The gradient subsystem is an essential part of an MRI system. Figures of merit for these systems include slew rate and the gradient field linearity. Our previously described 6.5 mT ultra-low-field MRI scanner has marginal gradient performance with low slew rates (minimal rise time of 750µs) and low efficiency (around 10µT/m/A). We describe here the optimization of a new gradient coil system with improved slew rate and efficiency. We introduce the equivalent magnetic dipole method to design biplanar gradient coils, and our design study of the geometric parameters of the gradient coil (including the coil pattern, its size and density).