A resistance random access memory (RRAM), based on a metal oxide thin film with resistive switching behavior, has been explored as an emerging candidate for their application as nonvolatile memories, due to their various advantages, such as simple device configuration, long data retention, high switching speed, and low operating voltage. Various metal oxides have been explored for resistive switching applications including, e.g., binary and ternary compounds. Among all metal oxides, the perovskites have attracted considerable interest due to their potential to be used for information storage and neuromorphic application. In this work, we demonstrate stable bipolar resistive switching devices based on the sputtered LaFeO<inline-formula> <tex-math notation="LaTeX">_{\text{3}}</tex-math> </inline-formula> thin film on fluorine doped tin oxide (FTO)-coated glass with circular-shaped silver contacts. The memory performance of fabricated devices was characterized as a function of the thickness of the LFO thin layer. The resistive switching properties are investigated using macroscopic <inline-formula> <tex-math notation="LaTeX">\textit{I}</tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">\textit{V}</tex-math> </inline-formula> measurements, showing low-voltage switching with a high ON-OFF ratio (<inline-formula> <tex-math notation="LaTeX">\approx </tex-math> </inline-formula>300) and long retention (<inline-formula> <tex-math notation="LaTeX">\ge </tex-math> </inline-formula>9000 s). The fabricated devices demonstrate the stable, low voltage and high-speed switching. Furthermore, in this work, we demonstrate the synaptic behavior of the LFO thin-film memory devices, as it exhibits analog memory characteristics, potentiation, and depression.