This Paper presents an automated method of Epileptic Spike detection in Electroencephalogram (EEG) using Deterministic Finite Automata (DFA). It takes pre-recorded single channel EEG data file as input and finds the occurrences of Epileptic Spikes data in it. The EEG signal was recorded at 256 Hz in two minutes separate data files using the Visual Lab-M software (ADLink Technology Inc., Taiwan). It was preprocessed for removal of baseline shift and band pass filtered using an infinite impulse response (IIR) Butterworth filter. A system, whose functionality was modeled with DFA, was designed. The system was tested with 10 EEG signal data files. The recognition rate of Epileptic Spike as on average was 95.68%. This system does not require any human intrusion. Also it does not need any short of training. The result shows that the application of DFA can be useful in detection of different characteristics present in EEG signals. This approach could be extended to a continuous data processing system.