Matrix gradient coils have received increasing interest in generating arbitrary-shaped magnetic fields for various magnetic resonance imaging applications. In this paper, a novel cone-shaped matrix gradient coil is proposed to design a multifunctional insertable system for head imaging. Using a volumetric finite-difference-based method, the matrix coil is designed to have comprised several coil elements that can implement localized imaging and control eddy current, dissipated power, and minimum wire gap. With the lowest total dissipated power, various current configurations are selected to generate multiple gradient fields within a large, spheroidal region of interest (ROI) and two small spherical sub-ROIs. The numerical computation results show that the designed matrix coil offers high flexibility in generating a local gradient field capable of improving the local resolution. In addition, with enhanced coil performance, the cone-shaped structure provides a patient-friendly solution for head imaging.