In this paper, we propose an efficient Artificial Neural Network (ANN) based on the global search capacity of evolutionary algorithms (EAs) to identify damages in laminated composite structures. With remarkable advances, ANN has taken off over the last decades. However, ANN also has major drawbacks relating to local minima issues because it applies backpropagation algorithms based on gradient descent (GD) techniques. This leads to a substantial reduction in the effectiveness and accuracy of ANN. Some researchers have been come up with some solutions to tackle the local minimal problems of ANN by looking for starting beneficial points to eliminate initial local minima based on the global search capacity of stochastic algorithms. Nevertheless, it is commonly acknowledged that those solutions are no longer useful or even counterproductive in some cases if the network contains too many local minima distributed deeply in the search space. Hence, we propose a novel approach applying the fast convergence speed of GD techniques of ANN and the global search capacity of EAs to train the network. The core idea is that EAs are employed to work parallel with ANN during the process of training the network. This guarantees that the network possibly determines the best solution fast and avoids getting stuck in local minima. To enhance the efficiency of the global search capacity, in this work, a hybrid metaheuristic optimization algorithm (HGACS) of EAs is also proposed, which possibly gains the advantages of both Genetic Algorithm (GA) and Cuckoo Search (CS). GA is applied to generate initial populations with the best quality derived from the ability of crossover and mutation operators, whereas CS with global search capacity is used to seek the best solution. Moreover, to deal with the large amount of data utilized to train the network, a vectorization technique is applied for the data of the objective function, which considerably decreases the computational cost. The obtained results prove that the proposed method is superior to traditional ANN, other hybrid-ANNs, and HGACS in terms of accuracy, and significantly reduces computational time compared with HGACS.