No, if you move away from the Earth, you will not eventually stop accelerating. In the absence of any external forces, an object in motion will continue to move with a constant velocity (including speed and direction) due to its inertia. This is described by Newton's first law of motion, also known as the law of inertia.
However, if you are referring to the acceleration due to Earth's gravity, then as you move farther away from the Earth, the gravitational force acting on you decreases with distance. According to Newton's law of universal gravitation, the force of gravity weakens as the distance between two objects increases. So while you will continue to experience the gravitational pull of the Earth, the strength of that gravitational force diminishes with distance.
Therefore, if you're already moving away from the Earth with a constant velocity, you will not experience any additional acceleration due to Earth's gravity. However, it's important to note that other celestial bodies in the solar system, such as the Sun or other planets, may exert gravitational forces that could affect your motion if you come within their gravitational influence.