Issues of asymptotic stabilization of the control systems without drift as given by the first derivative of x with respect to time = g(x)u are presented. Conditions of the existence of smooth time-invariant stabilizer for the general nonlinear systems are obtained, specifically, for the case of which the number of inputs is less than that of system states. This is achieved by constructing Jurdjevic-Quinn type Lyapunov function. Results do not contradict Brockett's necessary and sufficient condition for the existence of smooth time-invariant stabilizer. Sufficient conditions for system stabilizability are also attained for both bilinear systems and plannar homogeneous systems without drift.