Nanomaterials with ABX₃-type perovskite structure have attracted considerable and increasing attention due to their unique physical and chemical properties as well as promising applications in various fields. In this work, we have developed a simple electrospinning followed by a calcination process to prepare ABO₃-type perovskite LaMnO_3+δ nanofibers as efficient oxidase mimics for the detection of L-cysteine. The oxidase-like catalytic activity of the prepared LaMnO_3+δ nanofibers is heavily dependent on the calcination temperature which results in different sizes of the LaMnO_3+δ crystals and their crystallinity, and the maximum activity is achieved at the calcination temperature of 700 °C. Based on the high oxidase-like catalytic activity of the as-prepared perovskite LaMnO_3+δ nanofibers, a simple and accurate colorimetric detection method towards L-cysteine has been developed. The detection limit is as low as 109.8 nM and an excellent selectivity for L-cysteine detection with common substances in human blood as interferents is also achieved. In addition, the LaMnO_3+δ nanofibers can be retained as a monolithic membrane after the calcination process, making them an oxidase mimic for on-demand colorimetric sensing. This work reveals the promising prospects for the perovskite LaMnO_3+δ materials in biosensing, medical diagnosis, food safety and environmental monitoring.