This dissertation addresses the prediction based terminal velocity control guidance law which can control the terminal velocity of an aerial vehicle. Terminal velocity control problem is formulated into the two-point boundary value problem, and the guidance command is given by the acceleration command. This dissertation proposes a guidance law that satisfies the terminal velocity constraint through the pitch plane maneuver. It is inspired from the augmented polynomial guidance that can adjust the trajectory by changing a guidance constant without violating any other constraints. A terminal speed prediction method is provided that approximates the flight path into a polynomial function with the downrange-to-go terms to the power of (n+2), (m+2), 2, and 1, and a constant term. It assumes the acceleration command does not saturated along the path, then it is possible to integrate just velocity along the downrange to go. The proposed method keeps finding the guidance parameter updating periodically and controlling the terminal speed using the terminal speed prediction method. The acceleration to follow a parameterized curve is derived, and the polynomial approximating the path is employed to calculate the acceleration command in the terminal speed prediction process. Three strategies are proposed to determine the guidance parameter of APG according to the flight phase: First, it employs some numerical root finding algorithms to find the parameter. Second, the parameter is frequently updated using the predicted terminal velocity sensitivity and the slope of sensitivity. Third, if the terminal speed is unreachable, the guidance parameter is decided to maximize the terminal speed. Throughout the simulations, the sensitivity studies to the initial condition is studied in various conditions, and verified the terminal speed prediction accuracy. Finally it is demonstrated that the proposed guidance law can control the terminal speed.