In this work, the dependence of negative differential resistance (NDR) on compliance current (Icc) was investigated based on Ag/HfOx/Pt resistive memory device. Tunable conversion from bidirectional threshold switching (TS) to memory switching (MS) were achieved through enhancing Icc. NDR can be observed in TS as Icc is below 800μA but vanishes in MS. The switching voltages and readout windows of TS evolve with Icc. Furthermore, the dynamic conductance (dI/dV) as a function of time in NDR can be well illustrated by capacitor-like relaxation equation, and the relaxation time constant is significantly dependent on Icc. These phenomena were elucidated from viewpoint of nanofilament evolution controlled by Icc as well as nanocapacitor effects originated from nanofilament gap. The Icc-dependent NDR as well as conversion between TS and MS on Ag/HfOx/Pt resistive memory device indicates its potential application as a multifunctional electronic device.