Stiffness variation is useful in soft robots, especially for continuum manipulators which have a high slenderness ratio. Softness intrinsically gives robots high flexibility of movement, but stiffness gives the robots enough carrying capacity. Many types of continuum manipulators can change their stiffness; however, the both large-range and fast-response stiffness variation has not been realized. In this work, an omnidirectional steering flexible manipulator with large-range and fast-response stiffness variation was designed and fabricated. It was composed of a nested structure with a stiffness variation layer, a tendon-driven layer, and a transport channel. The stiffness variation was achieved by the phase transition of LMPA (Low-Melting Point Alloy) with a melting point of 50°C. Heating and cooling to the LMPA were performed by a tubular spring-like copper tube embedding in the LMPA. The tube not only acts as a skeleton of the manipulator, but also the material and structure of it bring the fast heat exchange. The motion of the manipulator was driven by tendons going through the holes of a threaded spring-like elastic skeleton which is flexible still can appropriately balance the self-weight of the manipulator. Continuum manipulators with one and two omnidirectional segments were fabricated to show the performance of movement and stiffness variation. Each segment is of 15 cm length and with diameter of 21 mm. The test shows that the stiffness of the manipulator has a factor of 45 variations in 15 seconds, and the stiffness variation is adequate to complete some challenging tasks like screw tightening and loosing.