We implement a wireless indoor navigation system based on the variational Gaussian process state-space model (GPSSM) with smartphone-collected WiFi received signal strength (RSS) and inertial measurement unit (IMU) readings. We adapt the existing variational GPSSM framework to wireless navigation scenarios, and provide a practical learning procedure for the variational GPSSM. The proposed system explores both the expressive power of the non-parametric Gaussian process model and its natural mechanism for integrating the state-of-the-art navigation techniques designed upon state-space model. Experimental results obtained from a real office environment validate the outstanding performance of the variational GPSSM in comparison with the traditional parametric state-space model in terms of navigation accuracy.