The integration of GPS and INS provides a system that has superior performance in comparison with either a GPS or an INS stand-alone systems. Most integrated GPS/INS positioning systems have been implemented using Kalman Filter (KF) technique. Although of being widely used, KF has some drawbacks related to computation load, immunity to noise effects and observability. In addition, KF only works well under certain predefined error models and provides accurate estimation of INS errors only during the availability of GPS signal. Upon losing the GPS signals, if the inertial sensor errors do not have an accurate stochastic model, Kalman filter delivers poor prediction of INS errors, and thus a considerable increase in position errors may be observed. The impact of these limitations affects the integrated system positional accuracy during GPS signal outages. Recently, the field of artificial intelligence has been receiving more attention in the development of alternative GPS/INS integration schemes. Therefore, in this paper, an alternative scheme is proposed which implements a Constructive Neural Network (CNN). The proposed scheme has flexible topology when compared to the recently utilized Multi-layer Feed-forward Neural Networks (MFNNs). The topologies of MFNN-based schemes are decided empirically with intensive training efforts and they remain fixed during navigation. In contrast, the proposed CNN scheme can adjust its architecture (i.e. the number of hidden neurons) autonomously during navigation based on the complexity of the problem in hand (i.e. dynamic variations) without the need for human intervention. The proposed scheme is implemented and tested using MEMS IMU data collected in land-vehicle environment. It does not require prior knowledge or empirical trials to implement the proposed architecture since it is able to adjust its architecture "on the fly" based on the complexity of the vehicle dynamic variations. This is a significant improvement compared to the previously developed MFNN scheme that requires extensive empirical trials. In addition, the proposed CNN architecture remains fixed after the final design. The proposed scheme performance is compared to both MFNN and KF during several GPS signal outages. The results of all schemes are then analyzed and discussed.