Mimicking synaptic plasticity is a key to harnessing the power of the brain. In the present work, manganese oxide (MnO2) thin films were developed by using the simple, low-cost hydrothermal method, and the hydrothermal deposition-time-dependent resistive switching property of MnO2 thin films was investigated. The current-voltage and the charge-magnetic flux characteristics suggested that the developed devices could be placed into the category of memristive devices. The bio-synaptic properties, such as synaptic weight, potentiation depression, and symmetric Hebbian learning of these devices were demonstrated. The developed devices were able to switch between two distinctly separable resistance states and to retain the resistive switching states for 103 s without any significant degradation. In addition, their non-zero current-voltage crossing property suggests that parasitic meminductance coexists with memristive behavior. For these devices, Schottky conduction mechanisms were found to be responsible for the resistive switching effect. The results of the present investigation should be very useful for neuromorphic computing applications.