Several approaches have been developed to cope with the limits of conventional origin-destination (O-D) trip matrix collecting methods. One is the bilevel programming method, which uses a sensitivity analysis-based (SAB) algorithm to solve a generalized least-squares problem. However, the SAB algorithm has revealed a critical shortcoming when there is a significant difference between the target O-D matrix and the true O-D matrix. This problem stems from the heavy dependence of the SAB algorithm on historical 0-D information. Such dependence may lead to a state in which the O-D estimator cannot produce a correct solution, especially when travel patterns are dramatically changed. To avoid the problem of dependency, a robust and stable method is required. A solution method is developed with a genetic algorithm, which is widely used in optimization problems to obtain a global solution. From the results of numerical examples, the proposed algorithm is superior to the SAB algorithm regardless of travel patterns.