During the deployment of practical applications, reservoir computing (RC) is highly susceptible to radiation effects, temperature changes, and other factors. Normal reservoirs are difficult to vouch for. To solve this problem, this paper proposed a random adaptive fault tolerance mechanism for an echo state network, i.e., RAFT-ESN, to handle the crash or Byzantine faults of reservoir neurons. In our consideration, the faulty neurons were automatically detected and located based on the abnormalities of reservoir state output. The synapses connected to them were adaptively disconnected and withdrawn from the current computational task. On the widely used time series with different sources and features, the experimental results show that our proposal can achieve an effective performance recovery in the case of reservoir neuron faults, including prediction accuracy and short-term memory capacity (MC). Additionally, its utility was validated by statistical distributions.