This paper describes the development of an innovative universal parallel gripper using a reformed magnetorheological (MR) fluid. The gripper has two fingertips, constructed using an elastic membrane enclosing the reformed MR fluid, which is stiffer than typical MR fluid. We developed a mechanism that moves a permanent magnet in order to control the viscosity of the reformed MR fluid, and an innovative elastic membrane to increase durability. The developed robot gripper grips and releases objects precisely, without excessive force, because the elastic parts can fit to the target shape. The gripper is driven quietly and can grip fragile and soft objects of various shapes. We performed numerous experiments to measure the gripping capacity of our gripper, and showed that it possesses force control, while also being able to move at high speeds.