Memristor, which is a nonlinear resistor with memory function, is the fourth fundamental two-terminal circuit element besides the resistor, capacitor and inductor. A memristor based oscillator circuit, directly derived from Chuas oscillator by replacing Chuas diode with a flux-controlled memristor characterized by a smooth monotonically increasing nonlinearity, is presented in this paper. By using conventional dynamical analysis method, the dynamical behaviors of the new smooth memristor oscillator with the variations of circuit parameters and initial conditions are investigated. The research results demonstrate that the dynamical behavior of the smooth memristor oscillator not only depends on the circuit parameters, but also closely depends on the initial conditions of the circuit. Different from general chaotic systems, some novel nonlinear phenomenas, such as the transient chaos and state transitions and so on, can be found in the proposed system.