The invention provides a movable anti-disengagement support. A control moving block is a hollow column, the lower end of the control moving block is fixedly connected with a lower support moving body, and the upper end of the control moving block is fixedly connected with an upper anti-disengagement control moving body; the upper anti-disengagement control moving body is of an annular structure; a lower anti-disengagement moving body is of a disc structure and is located in a cavity formed by a lower support moving body, the control moving block and the upper anti-disengagement control moving body; an anti-disengagement plate is of an annular structure and located between the lower anti-disengagement moving body and the upper anti-disengagement control moving body, the outer diameter of the anti-disengagement plate is larger than the inner diameter of the upper anti-disengagement control moving body, and the inner diameter of the anti-disengagement plate is smaller than the outer diameter of the lower anti-disengagement moving body; an anti-disengagement connecting part is of a column structure, the upper end of the anti-disengagement connecting part is fixedly connected with the lower surface of an upper moving body, and the lower end of the anti-disengagement connecting part penetrates through inner holes of the upper anti-disengagement control moving body and the anti-disengagement plate to be fixedly connected with the upper surface of the lower anti-disengagement moving body. According to the movable anti-disengagement support, disengagement does not occur in the moving process; movement inconsistent with the moving direction can be limited, and the stability of movement is improved; the amount of movement is limited, and the structure function is definite.