The macrospin model based on Landau-Lifshitz-Gilbert equation is used to study the current-induced magnetization dynamics in magnetic spin valves. We find that the DC spin-polarized current could either switch the magnetization of free layer or excite the steady-state precessional motion via the so-called spin-transfer torque effect. The AC current could drive the chaotic oscillations. The route to chaotic oscillation depending on the strength of current is demonstrated through a series of period doubling bifurcations.