In this paper, a S-type memristor with tangent nonlinearity is proposed. The introduced memristor can generate two kinds of stable pinched hysteresis loops with initial conditions from two flanks of the initial critical point. The power-off plot verifies that the memristor is nonvolatile, and the DC V-I plot shows that the memristor is locally active with the locally-active region symmetrical about the origin. The equivalent circuit of the memristor, derived by small-signal analysis method, is used to study the dynamics near the operating point in the locally-active region. Owing to the bistable and locally-active properties and S-type DC V-I curve, this memristor is called S-type BLAM for short. Then, a new Wien-bridge oscillator circuit is designed by substituting one of its resistances with S-type BLAM. It find that the circuit system can produce chaotic oscillation and complex dynamic behavior, which is further confirmed by analog circuit experiment.