No, if you are traveling close to the speed of light towards a light source, the light from the source will not appear to be moving towards you at twice the speed of light. According to Einstein's theory of special relativity, the speed of light in a vacuum is constant for all observers, regardless of their relative motion.
In the scenario you described, as you move close to the speed of light towards a stationary light source, the light emitted by the source will still propagate away from it at the speed of light. From your perspective, the light will approach you at the speed of light, not at a speed that is twice the speed of light.
Special relativity imposes a cosmic speed limit, the speed of light, which is approximately 299,792,458 meters per second. No observer, regardless of their motion relative to a light source, can measure the light from that source to be moving towards them at a speed faster than the speed of light.