Quantum-inspired Genetic Algorithm (QGA) is a probabilistic search optimization method combined quantum computation and genetic algorithm. In QGA, the chromosomes are encoded by qubits and are updated by quantum rotation gates, which can achieve a genetic search. Asset-based weapon target assignment (WTA) problem can be described as an optimization problem in which the defenders assign the weapons to hostile targets in order to maximize the value of a group of surviving assets threatened by the targets. It has already been proven that the WTA problem is NP-complete. In this study, we propose a QGA and a hybrid-QGA to solve an asset-based WTA problem. In the proposed QGA, a set of probabilistic superposition of qubits are coded and collapsed into a target number. Q-gate updating strategy is also used for search guidance. The hybrid-QGA is generated by incorporating both the random search capability of QGA and the evolution capability of genetic algorithm (GA). To observe the performance of each algorithm, we construct three synthetic WTA problems and check how each algorithm works on them. Simulation results show that all of the algorithm have good quality of solutions. Since the difference among mean resulting value is within 2%, we run the nonparametric pairwise Wilcoxon rank sum test for testing the equality of the means among the results. The Wilcoxon test reveals that GA has better quality than the others. In contrast, the simulation results indicate that hybrid-QGA and QGA is much faster than GA for the production of the same number of generations.