A flexible and transparent resistive switching memory based on a natural organic polymer for future flexible electronics is reported. The device has a coplanar structure of Mg/Ag-doped chitosan/Mg on plastic substrate, which shows promising nonvolatile memory characteristics for flexible memory applications. It can be easily fabricated using solution processes on flexible substrates at room temperature and indicates reliable memory operations. The elucidated origin of the bipolar resistive switching behavior is attributed to trap-related space-charge-limited conduction in high resistance state and filamentary conduction in low resistance state. The fabricated devices exhibit memory characteristics such as low power operation and long data retention. The proposed biocompatible memory device with transient electrodes is based on naturally abundant materials and is a promising candidate for low-cost memory applications. Devices with natural substrates such as chitosan and rice paper are also fabricated for fully biodegradable resistive switching memory. This work provides an important step toward developing a flexible resistive switching memory with natural polymer films for application in flexible and biodegradable nanoelectronic devices.