The controlled actuation of gallium liquid-metal (LM) alloys has presented new and exciting opportunities for constructing mobile robots with structural flexibility. However, the locomotion of current LM-based actuators often relies on inducing a gradient of interfacial tension on the LM surface within electrolytes, which limits their application outside a liquid environment. In this work, a wheeled robot using a LM droplet as the core of the driving system is developed that enables it to move outside liquid environment. The LM droplet inside the robot is actuated using a voltage to alter the robot's center of gravity, which in turn generates a rolling torque and induces continuous locomotion at a steady speed. A series of experiments is carried out to examine the robot's performance and then to develop a dynamic model using the Lagrange method to understand the locomotion. An untethered and self-powered wheeled robot that utilizes mini-lithium-batteries is also demonstrated. This study is envisaged to have the potential to expand current research on LM-based actuators to realize future complex robotic systems.