The construction of an organic-electronic resistive switch based on polymer electrolytes is the basis to study the interfacial and bulk transport as well as the interaction between ions and electrons/holes at the nanoscale level. Moreover, it could also be potentially applied in novel nanoelectrochemical devices for sensors, fuel cells and batteries, and therefore has attracted much attention in recent years. In this work, we fabricated resistive switching devices with silver-ion-conductive polymer electrolytes. The devices showed bipolar switching behaviors in the current-voltage characteristics for different silver ion concentrations ranging from 1 to 4 wt%. A high resistance up to 1 GΩ in the OFF state and a low resistance with less than tens of kΩ in the ON state can be achieved. We believe that the observed switching results from formation and annihilation of Ag metal filaments inside the polymer film by solid electrochemical reaction. Sequential operations, such as write-read-erase-read, were also demonstrated.