In this paper, we study an HP TiO2 memristor model with a parasitic memcapacitor, and it is shown that the parasitic element has significant effects on the volt-ampere characteristics and the dynamics of the memristor circuits. Further, the study shows that the pinched point on the hysteresis loop of the HP TiO2 memristor may deviate from the origin. We also show that the memristor with a parasitic memcapacitor will eventually lose its stored flux when its power is switched off. Furthermore, in order to study the parasitic effects in circuits, we derive a simple three-element series circuit that contains an inductor, a negative resistor, and an HP TiO2 memristor. If the parasitic memcapacitor of the memristor is considered, we observe a parasitic periodic oscillation occurred in the circuit.