We investigate a model of randomly copuled neurons. The elements are FitzHgh-Nagumo excitable neurons. The interactions between them are the mixture of excitatory and inhibitory. When all interactions are excitatory, a rest state is globally stable due to the excitability of neurons. Increasing the number of inhibitory connections, we observe the phase transition from the rest state to an oscillatory state. An analytical description for the critical point of the transition is obtained by means of random matrix theories for an infinite number of neurons, and the result is in good agreement with numerical simulation.