We have studied the secular motion of a single ion stored in a Paul trap and sub jected to a sequence of standing laser pulses. Through theoretical analyses and numerical calculations, we obtain an exact solution of the classical motion equa tion that describes time evolution of the system. By using the exact solution we have investigated regular and chaotic motions of the system. For a weakly trapp ed ion with small confining frequency, a critical condition under which the s ys tem goes into global chaos is found. The loss of stability caused by resonanc e is shown and a method for controlling the instability is established.