This paper proposes a new Initial CCT (Critical Clearing Time) estimation method using a hybrid neural network composed of iRprop (Improving the Resilient back PROPation Algorithm) and RAN (Resource Allocation Network). In transient stability study, CCT evaluation is very important but time consuming due to the fact it needs many iteration of time domain simulations gradually increasing the fault clearing time. The key to reduce the required computing time in this process is to find accurate initial estimation of CCT by a certain handy method before going to the iterative stage. As one of the strongest candidates of this handy method is the utilization of the pattern recognition ability of neural networks, which enable us to jump to a close estimation of the real CCT without any heavy computing burden. This paper proposes a new hybrid neural network which is a combination of the well-known iRprop and RAN. In the proposed method, the outputs of the hidden units of RAN are modified by multiplying the contribution factors calculated by an additional iRprop network. Numerical studies are done using two different test systems for the purpose of confirming the validity of the proposal. The result of the proposed method is the best. Properly evaluating the contribution of each input to the hidden units, the estimation error obtained by the proposed method is improved further than the original RAN based estimation.